Reaction-diffusion equations and the Laplacian in Hilbert space.

Abstract

This dissertation consists of two parts. First, we study some problems associated with reaction-diffusion equations with variables in finite-dimensional space. We investigate the positivity of solutions, the existence of positive invariant regions, and we also make some stability analysis. In part II, we study the Levy-Laplacian in infinite-dimensional space. We explore some properties of this Laplacian and solve some boundary value problems.