On Existence and Nonexistence Global Solutions of Reaction-Diffusion Equations

Existence and Nonexistence of Global Solutions of a Weakly Coupled System of Reaction-Diffusion Equations

Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms

We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for the nonexistence we extend the conditions of the nonlinear terms and the initial data to the weaker conditions. We prove that for the nonlinear term and the initial data whose support is included in som...

Global dynamics for a class of non-monotone time-delayed reaction-diffusion equations

This paper deals with a large class of non-monotone time-delayed reaction-diffusion equations in which the reaction term can be spatially nonlocal. Nonexistence, existence, uniqueness and global attractivity of positive equilibriums to the equation are addressed. In particular, developed is a technique that combines the method of super-sub solutions, the variation-of-constants formula for the d...

Existence of Global Solutions in Time for Reaction-Diffusion Systems with Inhomogeneous Terms in Cones

We consider nonnegative solutions of the initial-boundary value problems in cone domains for the reaction-diffusion systems with inhomogeneous terms dependent on space coordinates and times. In our previous paper the conditions for the nonexistence of global solutions in time were shown. In this paper we show the condition of existence of global solutions in time.

Blow up of solutions to generalized Keller–Segel model

The existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve Lévy diffusion operators and general potential type nonlinear terms.