We give an exhaustive characterization of singular weak solutions for some singular ordinary differential equations. Our motivation stems from the fact that in the context of hydrodynamics several prominent equations are reducible to an equation of this form upon passing to a moving frame. We construct peaked and cusped waves, fronts with finite-time decay and compact solitary waves. We prove that one cannot obtain peaked and compactly supported traveling waves for the same equation. In particular, a peaked traveling wave cannot have compact
support and vice versa. To exemplify the approach we apply our results to the Camassa-Holm equation and the equation for surface waves of moderate amplitude, and show how the different types of singular solutions
can be obtained varying the energy level of the corresponding planar Hamiltonian systems.
Our aim in this paper is to study a generalization of the conserved Caginalp phase-field system based on the Maxwell–Cattaneo law for heat conduction and endowed with Neumann boundary conditions. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators.
Our aim in this paper is to study a generalization of the conserved Caginalp phasefield
system based on the Maxwell–Cattaneo law for heat conduction and endowed with
Neumann boundary conditions. In particular, we obtain well-posedness results and study
the dissipativity of the associated solution operators.
Our aim in this article is to study a Caginalp phase-field system based on a thermomechanical
theory of deformable continua proposed by Green and Naghdi (called type III
thermoelasticity) and with a nonlinear coupling. In particular, we prove the existence and
uniqueness of solutions and the dissipativity of the associated semigroup. We then study
the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.
Grau, M.; Noguera, M.; Diaz-Barrero, J.L.; Peris, J. Nonlinear analysis: real world applications Vol. 11, num. 1, p. 414-422 DOI: 10.1016/j.nonrwa.2008.11.013 Data de publicació: 2010-02-01 Article en revista
This work models the dynamics and evolution of carbon (C) and nitrogen (N) related to organic matter in soils by using individual-based simulations. The simulator INDISIM-SOM controls a group of microbial cells at each time step, using a set of time-dependent variables for each microorganism. The space is divided into square cells. In each spatial cell, the amounts of different types of organic compounds are controlled. These are identified as polymerized organic C and N, labile organic C and N, mineral compounds likeNNH4,NNO3,CO2 andO2. The model takes into account the activity of two prototypes of microbial cells: ammonifier microorganisms and nitrifier bacteria. Different metabolic pathways and sources of C and N they can use are identified. Some state variables and parameters related to soil organic matter and microbial activity: growth and decay of microbial biomass, and
temporal evolutions of mineralized intermediate N, mineral N in ammonium and nitrate, CO2 and O2 are studied. The calibration of the simulation model has made use of data from laboratory incubation
experiments performed on two different types of Mediterranean soils. Both, conceptual validation during the development of the model and agreement of the simulation results with experimental.