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 first and the last layers. We also allow the possibility of having Dirichlet, Newman or mixed type conditions in the first and the last layers. We express the solutions in terms of variation of constants formula. Our approach constitutes a first step in order to deal with multilayer reaction-diffusion problem with non-local boundary value conditions by using integrated semigroup theory.

Mathematics Subject Classification (2020):

• 47D06
• 35K57
• 35Q79

Key words:

• Multilayer reaction-diffusion
• semigroup
• integrated solution
• non-homogeneous boundary