In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.
The final publication is available at link.springer.com via https://doi.org/10.1007/s00245-017-9439-8
Our aim in this article is to study a phase-field system based on a three-phase-lag for the termal flux vector. In particular, we prove the existence and uniqueness of solutions and then study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.