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  • Heat transfer analysis of nanofluids and phase change materials

     De Decker, Michelle Mari
    Defense's date: 2014-02-14
    Universitat Politècnica de Catalunya
    Theses

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    La nanotecnología va conquistando el mundo día a día, de dentro hacia fuera, tal y como Richard Feynman proclamó en sucharla titulada ¿There is plenty of room at the bottom¿ (Hay mucho espacio vacío allí abajo) en la década de los 50.Actualmente, la nanotecnología tiene impacto sobre multitud de áreas incluyendo medicina, producción y almacenamientode energía, etc. La investigación nanotecnológica es primordial en campos como la química, la física, la biotecnología y laingeniería. Hasta el momento, la modelización matemática ha tenido un rol minoritario en este campo. Uno de los objetivosprincipales de esta tesis es compensar este desequilibrio. La parte final de la tesis trata sobre tres problemas relacionadoscon la modelización de fenómenos en la nanoescala. Los diferentes capítulos de la tesis tienen un denominador común: eluso del ¿Heat Balance Integral Method¿ (HBIM), un método para encontrar soluciones aproximadas que ha permitidoprogresar en el estudio analítico de los diferentes modelos.El capítulo 2 contiene una descripción y validación completa de la versión estándar del HBIM en coordenadas cartesianas.En el capítulo 3 el HBIM y sus variantes se aplican al problema de Stefan en geometría esférica y cilíndrica. Se observacomo una transformación sobre el dominio del problema mejora notablemente la eficacia de este método. Los resultadosobtenidos se utilizan en los siguientes capítulos.En el capítulo 4 se desarrolla un modelo que describe el cambio de fase de un cubo al ser calentado en su superficie,proceso que se utiliza en sistemas de almacenamiento de frío. Los resultados muestran como evoluciona el cambio defase. Al comparar las soluciones del modelo con datos experimentales los resultados son excelentes.En el capítulo 5 se introduce el concepto de nanofluido. Se investiga la estabilidad de las nanopartículas suspendidas en unfluido, se presenta un debate sobre la validez del continuo en la nanoescala y se describen las propiedades físicas de unnanofluido. También se detalla como se modelizan las propiedades de estos fluidos. En el capítulo 6 se deriva unaexpresión analítica simple para la conductividad térmica y la difusividad de un nanofluido. El modelo describe con precisiónuna amplia gama de datos experimentales y predice valores significativamente mayores que el modelo clásico de Maxwell,el cual no se ajusta a los datos.El capítulo 7 contiene un análisis del flujo en la capa límite del nanofluido. Se demuestra como el movimiento browniano y latermofóresis son irrelevantes como mecanismos de transmisión del calor y como el coeficiente de transmisión del calordecrece con la concentración de nanopartículas, contrariamente a los resultados obtenidos en estudios. En consecuencia,en la sección final del capítulo se debaten los errores de algunos de los artículos más citados en este campo.En el capítulo 8 se considera un nanofluido como el material de cambio de fase (¿phase change material¿, PCM) en unproceso de fusión por contacto (¿contact melting¿). Se modifica el modelo del capítulo 4 para que tenga en cuenta laspropiedades termo-físicas variantes del nanofluido. Se analiza el tiempo total de cambio de fase y la velocidad del proceso.Se observa que las ventajas del uso de nanofluidos como PCM en este tipo de procesos depende del tamaño del sistema,lo cual cuestiona los aclamados beneficios de los nanofluidos como innovadores PCMs.En el capítulo 8 se considera un nanofluido como el material de cambio de fase en un proceso de fusión por contacto. Semodifica el modelo del capítulo 4 para que tenga en cuenta las propiedades termo-físicas variantes del nanofluido. Seanaliza el tiempo total de cambio de fase y la velocidad del proceso. Se observa que las ventajas del uso de nanofluidoscomo material de cambio de fase en este tipo de procesos depende del tamaño del sistema, lo cual cuestiona losaclamados beneficios de los nanofluidos como innovadores materiales de cambio de fase.

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    Known results and open problems on C1 linearization in Banach spaces  Open access

     Munhoz Rodrigues, Hildebrando; Sola-morales Rubio, Juan de La Cruz de
    The Sao Paulo Journal of Mathematical Sciences
    Date of publication: 2012
    Journal article

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    The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C1 case, and also to present some open problems that we believe that are still important for the understanding of the theory

    The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open problems that we believe that are still important for the understanding of the theory.

  • On the diffusion algorithm for density-equalizing maps with piecewise constant initial data

     Avinyó, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Mathematical methods in the applied sciences
    Date of publication: 2012-07-15
    Journal article

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    We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration).

    We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration).

  • On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

     Aguareles Carrero, Maria; Haro Cases, Jaime; Rius Vazquez, Jose; Sola-morales Rubio, Juan de La Cruz de
    European journal of applied mathematics
    Date of publication: 2012-04
    Journal article

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  • Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos

     Lubary Martinez, Jose Antonio; Gonzalez Nogueras, Maria Del Mar; Haro Cases, Jaime; Sola-morales Rubio, Juan de La Cruz de; Consul Porras, M. Nieves; Cabre Vilagut, Xavier
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  • A singular initial value problem to construct density-equalizing maps

     Avinyó, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Journal of dynamics and differential equations
    Date of publication: 2011-12
    Journal article

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    The diffusion-based algorithm to produce density-equalizing maps interprets diffusion as an advection process. This algorithm uses the dynamics of a flow that is defined by an initial value problem that turns out to be very singular at the initial time. The singularities appear when the initial density has line or angle discontinuities, which is always the case, for example, in area cartogram maps. This singular initial value problem is analyzed mathematically in this article and the conclusion is that despite these singularities, it has a unique solution. This justifies the extensive numerical use of this algorithm in the recent years. The techniques presented in this article use both partial and ordinary differential equations estimates.

  • Access to the full text
    A singular initial value problem to construct density-equalizing maps  Open access

     Avinyó, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Date: 2011-05
    Report

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    The diffusion-based algorithm to produce density-equalizing maps interprets diffusion as an advection process. This algorithm uses the dynamics of a flow that is defined by an initial value problem that turns out to be very singular at the initial time. The singularities appear when the initial density has line or angle discontinuities, which is always the case, for example, in area cartogram maps. This singular initial value problem is analyzed mathematically in this paper and the conclusion is that despite these singularities, it has a unique solution. This justifies the extensive numerical use of this algorithm in the recent years. The techniques presented in this paper use both partial and ordinary differential equations estimates.

  • On the Hartman¿Grobman Theorem with Parameters

     M. Rodrigues, Hildebrando; Sola-morales Rubio, Juan de La Cruz de
    Journal of dynamics and differential equations
    Date of publication: 2010
    Journal article

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  • Bistable elliptic equations with fractional diffusion

     Cinti, Eleonora
    Defense's date: 2010-07-05
    Department of Applied Mathematics I, Universitat Politècnica de Catalunya
    Theses

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  • EQUACIONS DIFERENCIALS EN DERIVADES PARCIALS I APLICACIONS

     Sola-morales Rubio, Juan de La Cruz de; Mande Nieto, Jose Vicente; Lubary Martinez, Jose Antonio; Consul Porras, M. Nieves; Aguareles Carrero, Maria; Valencia Guitart, Marta; Haro Cases, Jaime; Lucia D'Agostino, Marcello; Gonzalez Nogueras, Maria Del Mar; Cabre Vilagut, Xavier
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    A note on the relationship between spectral radius and norms of bounded linear operators  Open access

     Munhoz Rodrigues, Hildebrando; Sola-morales Rubio, Juan de La Cruz de
    Matemática contemporânea
    Date of publication: 2009
    Journal article

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    Let X be a Banach space and L ( X ) be the Banach algebra of bounded operators on X . In this note we prove that if we have a compact subset K of a commutative sub-algebra of L ( X ), and given " > 0, then it is possible to de ne a new norm in X , equivalent to its given norm, in such a way that inside a neighborhood U " of this compact set in the sub- algebra, the norms of all the operators di er from their spectral radius in less than " . If X is a Hilbert space then it is possible to de ne this new norm as an Hilbertian norm.

  • ECUACIONES EN DERIVADAS PARCIALES; ANÁLISIS Y APLICACIONES

     Sola-morales Rubio, Juan de La Cruz de; Mande Nieto, Jose Vicente; Lubary Martinez, Jose Antonio; Consul Porras, M. Nieves; Aguareles Carrero, Maria; Valencia Guitart, Marta; Haro Cases, Jaime; Lucia D'Agostino, Marcello; Gonzalez Nogueras, Maria Del Mar; Cabre Vilagut, Xavier
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  • Optimal decay rates and the selfadjoint property in overdamped systems

     Pellicer, M; Sola-morales Rubio, Juan de La Cruz de; Pellicer, Marta
    Journal of differential equations
    Date of publication: 2009-04
    Journal article

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  • Spectral analysis and limit behaviours in a spring-mass system

     Sola-morales Rubio, Juan de La Cruz de; Pellicer, Marta
    Communications on pure and applied analysis
    Date of publication: 2008
    Journal article

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    We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE.

  • Asymptotic Behavior in an Elliptic Problem with Nonlinear Dynamic Boundary Conditions

     Sola-morales Rubio, Juan de La Cruz de
    Sumer Meeting on Diferential Equations
    Presentation's date: 2008-02-01
    Presentation of work at congresses

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  • On the Hartman-Grobman Theorem with Parameters

     Sola-morales Rubio, Juan de La Cruz de
    Date: 2008-01
    Report

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  • Spectral analysis and limit behaviours in a spring-mass system

     Sola-morales Rubio, Juan de La Cruz de
    Communications on pure and applied mathematics
    Date of publication: 2008-01
    Journal article

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  • Interaction of spiral waves in the general complex Ginzburg-Landau equation  Open access

     Aguareles Carrero, Maria
    Defense's date: 2007-07-23
    Department of Applied Mathematics I, Universitat Politècnica de Catalunya
    Theses

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    Molts sistemes físics tenen la propietat que la seva dinàmica ve definida per algun tipus de difussió espaial en competició amb un fenòmen de reacció, com per exemple en el cas de dos components químics que reaccionen al mateix temps que es difon l'un en el si de l'altre. La presència d'aquests dos fenòmens, la difusió i la reacció, sovint dóna lloc a patrons no homogenis de gran riquesa. Els models matemàtics que descriuen aquest tipus de comportament són normalment equacions en derivades parcials les solucions de les quals representen aquests patrons. En aquesta tesi s'analitza l'equació de Ginzburg-Landau complexa general, que és una equació en derivades parcials de reacció-difusió que s'utilitza sovint com a model matemàtic per a descriure sistemes oscil·latoris en dominis extensos. En particular estudiem els patrons que sorgeixen en el pla quan s'imposa que el grau de Brouwer de la solució no sigui nul. Aquests patrons estan formats per ones de rotació en forma d'espirals, és a dir, les corbes de nivell de la solució formen espirals que emanen dels punts on la funció s'anul·la. Quan la solució s'anul·la només en un punt i per tant només hi ha una espiral, tota la dependència temporal apareix en el terme de freqüència. Així doncs, la funció solució es pot expressar com a funció del radi polar i en termes del seu grau topològic i la freqüència de l'ona. Per tant, aquestes solucions es poden expressar en termes d'un sistema d'equacions diferencials ordinàries. Aquestes solucions només existeixen per una certa freqüència que depèn unívocament dels paràmetres de l'equació i, com a conseqüència i degut a la relació de dispersió entre el nombre d'ones i la freqüència, el nombre d'ones a l'infinit, l'anomenat nombre d'ones asimptòtic, ve també determinat unívocament pels paràmetres. Quan les solucions tenen més d'un zero aïllat la condició sobre el grau de la funció fa que de cada zero sorgeixi una espiral diferent i aquestes es mouen en el pla mantenint la seva estructura local. En aquest treball s'usen tècniques d'anàlisi asimptòtica per trobar equacions del moviment per als centres de les espirals i es troba que aquesta evolució temporal és lenta. En concret, per la distàncies relatives grans entre els centres de les espirals, l'escala de temps per a la seva dinàmica ve donada pel logaritme de l'invers d'aquesta distància. Es demostra que aquestes equacions del moviment són diferents en funció de la relació entre els paràmetres de l'equació de Ginzburg-Landau complexa i la separació entre els centres de les espirals, i que la forma com es passa d'unes equacions a les altres és molt singular. També es demostra que el nombre d'ones asimptòtic per al cas de sistemes amb diverses espirals també està unívocament determinat pels paràmetres però no obstant, el cas de sistemes amb diverses espirals es diferencia del cas d'una única ona en què deixa de ser constant i evoluciona al mateix ritme que la velocitat dels centres de les espirals.

    Many physical systems have the property that its dynamics is driven by some kind of spatical diffusion that is in competition with a reaction, like for instance two chemical species that react at the same time that there is a diffusion of each of them into the other. This interplay between reaction and diffusion produce non-homogeneous patterns that can sometimes be very rich. The mathematical models that describe this kind of behaviours are usually nonlinear partial differential equations whose solutions represent these patterns. In this thesis we focus on an especific reaction-diffusion equation that is the so-called general complex Ginzburg-Landau equation that is used as a model for oscillatory systems in extended domains. In particular we are interested in the type of patterns in the plane that arise when the solutions have a non-vanishing Brouwer degree. These patterns have the property that they exhibit rotating waves in the shape of spirals, which means that the contour lines arrange in the shape of spirals that emerge from the points where the solution vanishes. When the solution vanishes only at one point all the time dependence appears as a frequency term so the solutions can be expressed as a function of the polar radius and in terms of the topological degree of the solution and the frequency of the wave. Therefore, these solutions can be expressed in terms of a system of ordinary differential equations. These solutions do only exist with a given frequency, and as a consequence and due to the existence of a dispresion relation, the wavenumber far from the origin, the so-called asymptotic wavenumber, is also unique. When the solutions have more than one isolated zero, the condition on the degree of the function has the effect of producing several spirals that emerge from the different zeros of the solution. These spirals evolve in time keeping their structure but moving around on the plane. In this work we use asymptotic analysis techniques to derive laws of motion for the centres of the spirals and we show that the time evolution of these patterns is slow and, for large relative separations of the centres of the spirals, the time scale for the their dynamics is logarithmic in the inverse of this distance. These laws of motion are different depending on the relation between the parameters of the complex Ginzburg-Landau equation and the relative separation of the spirals. We show that the way these laws change as the spirals separate or approach is highly singular. We also show that the asymptotic wavenumber in the case of multiple spirals is as well unique and that it evolves in time at the same rate as the velocity of the centres.

  • Les equacions d'Euler dels fluids no viscosos

     Sola-morales Rubio, Juan de La Cruz de
    Date of publication: 2007-06-30
    Book chapter

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  • Transformations with given jacobians

     Sola-morales Rubio, Juan de La Cruz de
    British Applied Mathematics Colloquium
    Presentation's date: 2006-01-01
    Presentation of work at congresses

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  • Laplace's equation in the half-space witn nonlinear boundary conditions.

     Sola-morales Rubio, Juan de La Cruz de
    Sumer Meeting on Diferential Equations
    Presentation's date: 2006-02-01
    Presentation of work at congresses

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  • Invertible contractions and asymptotically stable ODE's that are not C1-linearizable

     Sola-morales Rubio, Juan de La Cruz de
    Journal of dynamics and differential equations
    Date of publication: 2006-01
    Journal article

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  • Layer solutions in a half-space for boundary reactions

     Cabre Vilagut, Xavier; Sola-morales Rubio, Juan de La Cruz de
    Communications on pure and applied mathematics
    Date of publication: 2005-12
    Journal article

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  • Viscoelastic and non-viscoelastic spring-mass models

     Sola-morales Rubio, Juan de La Cruz de
    Workshop on Partial Differential Equations, Optimal Design and Numerics 2005
    Presentation's date: 2005-08-28
    Presentation of work at congresses

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  • Laplace's equation with nonlinear boundary conditions

     Sola-morales Rubio, Juan de La Cruz de
    EMS-SCM Joint Mathematical Weekend
    Presentation's date: 2005-09-16
    Presentation of work at congresses

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  • An Invertible Contraction that is not C1-linearizable

     Sola-morales Rubio, Juan de La Cruz de
    Rencontre de Systèmes Dynamiques en Dimension Infinie
    Presentation's date: 2005-07-04
    Presentation of work at congresses

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  • Ecuaciones en derivadas parciales y aplicaciones: problemas de evolución y de reacción-difusión

     Cabre Vilagut, Xavier; Valencia Guitart, Marta; Blasco Lorente, Jorge; Aguareles Carrero, Maria; Sola-morales Rubio, Juan de La Cruz de; Gonzalez Nogueras, Maria Del Mar; Haro Cases, Jaime
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  • Viscosidad interna y comportamiento límite en una ecuación de ondas con disipación fuerte

     Sola-morales Rubio, Juan de La Cruz de
    Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
    Presentation's date: 2005-09-19
    Presentation of work at congresses

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  • Viscoelastic and non-viscoelastic spring-mass models

     Sola-morales Rubio, Juan de La Cruz de
    Congreso Conjunto de Matemáticas RSME-SCM-SEIO-SEMA
    Presentation's date: 2005-01-31
    Presentation of work at congresses

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  • An invertible contraction that is not C1-linearizable

     Rodrigues, H M; Sola-morales Rubio, Juan de La Cruz de
    Comptes rendus de l'Académie des sciences. Série 1, Mathématique
    Date of publication: 2005-06
    Journal article

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  • Análisis de un modelo de suspensión-amortiguación

     Pellicer Sabadi, Marta
    Defense's date: 2004-09-17
    Department of Applied Mathematics I, Universitat Politècnica de Catalunya
    Theses

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  • Analysis of a viscoelastic spring-mass model

     Pellicer Sabadi, Marta; Sola-morales Rubio, Juan de La Cruz de
    Journal of mathematical analysis and applications
    Date of publication: 2004-06
    Journal article

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  • Linearization of class C1 for contractions on Banach Spaces

     Rodrigues, Munhoz H; Sola-morales Rubio, Juan de La Cruz de
    Journal of differential equations
    Date of publication: 2004-07
    Journal article

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  • Smooth linearization for a saddle on Banach spaces

     Rodrigues, H; Sola-morales Rubio, Juan de La Cruz de
    Journal of dynamics and differential equations
    Date of publication: 2004-07
    Journal article

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  • On maps with given jacobians involving the heat equation

     Avinyó Andrés, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Zeitschrift für angewandte Mathematik und Physik
    Date of publication: 2003-11
    Journal article

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  • Properties of a viscoelastic spring-mass system

     Sola-morales Rubio, Juan de La Cruz de
    ICMC Summer Meeting in Differential Equations. 2003 Chapter
    Presentation's date: 2003-02-04
    Presentation of work at congresses

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  • Maps with given Jacobian and the heat equation

     Sola-morales Rubio, Juan de La Cruz de
    5èmes Journées des EDP Littoral-Valenciennes
    Presentation's date: 2003-09-24
    Presentation of work at congresses

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  • Regularity of a map with a given jacobian involving the heat equation

     Avinyó Andrés, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Date of publication: 2003-01
    Book chapter

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  • Regularity of a map with a given jacobian involving the heat equation

     Avinyó Andrés, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
    Presentation of work at congresses

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  • Anàlisi i resolució de problemes amb origen físic, biològic i geomètric modelats per EDP.

     Consul Porras, M. Nieves; Sola-morales Rubio, Juan de La Cruz de
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  • Red Temática: Análisis y resolución de problemas con origen físico, biológico y geométrico modelados por ecuaciones en derivadas parciales

     Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta; Cabre Vilagut, Xavier
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  • Regularity of a map with a given jacobian involving the heat equation

     Sola-morales Rubio, Juan de La Cruz de
    Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
    Presentation's date: 2003-09-18
    Presentation of work at congresses

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  • Regularity of a map with a given jacobian involving the heat equation

     Avinyó Andrés, Albert; Sola-morales Rubio, Juan de La Cruz de; Valencia Guitart, Marta
    Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
    Presentation of work at congresses

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  • Ecuaciones en Derivadas Parciales: problemeas de evolución, problemas geométricos, modelización y aplicaciones

     Consul Porras, M. Nieves; Sola-morales Rubio, Juan de La Cruz de
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  • GRUPS D´ESTUDI DE MATEMÀTICA I TECNOLOGIA, GEMT

     Sola-morales Rubio, Juan de La Cruz de
    Participation in a competitive project

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  • Ecuaciones en Derivadas Parciales: problemas de evolución, problemas geométricos, modelización y aplicaciones

     Valencia Guitart, Marta; Sola-morales Rubio, Juan de La Cruz de; Blasco Lorente, Jorge; Aguareles Carrero, Maria; Cabre Vilagut, Xavier; Haro Cases, Jaime
    Participation in a competitive project

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