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.

中文翻译：

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关于多层反应扩散问题：半群方法，第一部分

摘要

我们使用半群理论来获得多层扩散模型解的存在性和唯一性，这些模型可能具有非线性反应项以及第一层和最后一层的局部非齐次边界条件。我们还允许在第一层和最后一层使用 Dirichlet、Newman 或混合类型条件。我们用常数公式的变化来表达解决方案。我们的方法是利用集成半群理论处理具有非局部边值条件的多层反应扩散问题的第一步。