On multilayer reaction-diffusion problems: A semigroup approach, Part I

Abstract

We use the theory of semigroups to obtain the existence and uniqueness of solutions for multilayer diffusion models with possibly non linear  reactions terms as well as local non-homogeneous boundary conditions on the rst and the last layers. We also allow the possibility of having Dirichlet,  Newman or mixed type conditions in the rst and the last layers. We express the solutions in terms of variation of constants formula. Our approach  constitutes a rst step in order to deal  with multilayer reaction-diffusion problem with non-local boundary value conditions by using integrated semigroup theory.