Spatial decay in mixtures of heat conductive rigid solids as an evolutive problem

Abstract

The objective of this article is to study the spatial behavior of solutions in the case of heat conduction in a static cylinder for a mixture of rigid solids. Although this question is an ill-posed problem in the Hadamard sense, since there is no uniqueness of solutions nor continuous dependence on initial data, we focus on the study of decaying solutions. When we restrict to this class of functions, we obtain a well-posed problem. We will show that we can see the solutions through an analytic semigroup structure, for which the long variable acts as the evolution variable. Therefore, we can apply the properties of these semigroups. Finally, we also consider the case in which a certain type of supply terms is introduced, and the solutions are obtained with the help of semigroups theory. A few comments for alternative boundary conditions are also considered.

Peer Reviewed

Postprint (published version)