On quenching of solutions to nonautonomous semilinear parabolic equations and reaction—diffusion systems

Abstract

Dedicated to the memory of Professor E.M.Landis

A solution of a nonlinear evolution problem is said to display quenching if in finite time this solution attains a value such that one of the terms forming the problem ceases to make sense. This phenomenon has been studied by a lot of authors for various scalar autonomous partial differential equations. In the present paper, we analyse several examples concerned with quenching of solutions to nonautonomous nonlinear equations of parabolic type and nonlinear parabolic systems. Specifically, we construct a reaction-diffusion system such that some of its spatially nonhomogeneous solutions display quenching, while all solutions to the corresponding system of ordinary differential equations are global.

Keywords:

• Nonlinear parabolic problems
• quenching
• global existence