- 17-98 Vitaly Volpert, Vitali Vougalter
- Method of monotone solutions for reaction-diffusion equations
Sep 14, 17
(auto. generated pdf),
of related papers
Abstract. Existence of solutions of reaction-diffusion systems of equations in unbounded domains is studied by the Leray-Schauder (LS) method based on
the topological degree for elliptic operators in unbounded domains and on
a priori estimates of solutions in weighted spaces. We identify some
reaction-diffusion systems for which there exist two sub-classes of solutions separated in the function space, monotone and non-monotone
solutions. A priori estimates and existence of solutions are obtained
for monotone solutions allowing to prove their existence by the LS method.
Various applications of this method are given.