On the properties of generalized solutions of a nonlinear Cauchy problem for a nonlinear parabolic system with absorption or source

Abstract

This paper deals with the existence and nonexistence of global positive solutions of quasilinear reaction diffusion systems with nonlinear boundary conditions. The properties of generalized solutions of one nonlinear self-similar system of equations are investigated. A condition for global solvability of Fujita type is obtained, generalizing the result of [1]. The asymptotic behavior of the eigenfunction of a nonlinear two-component medium is established. Based on them, numerical calculations were carried out.