Semilinear reaction-diffusion systems with nonlocal sources

Blowup Properties for a Semilinear Reaction-Diffusion System with Nonlinear Nonlocal Boundary Conditions

and Applied Analysis 3 1, 2, 6–9 and the references cited therein . For blowup results for other parabolic systems, we refer the readers to 10–13 and the references cited therein. Moreover, in recent years, many authors see studies such as those in 14, 15 and the references cited therein considered semilinear reaction-diffusion systems with nonlocal Dirichlet boundary conditions of the form ut ...

Global existence for semilinear reaction-diffusion systems on evolving domains.

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that comm...

Blowup Analysis for a Nonlocal Reaction Diffusion Equation with Potential

In this paper we investigate a nonlocal reaction diffusion equation with potential, under Neumann boundary. We obtain the complete classification of the parameters for which the solution blows up in finite time or exists globally. Moreover, we study the blowup rate and the blowup set for the blowup solution. Key–Words: Nonlocal diffusion, Blow up, Blowup rate, Blowup set

Semilinear Nonlocal Differential Equations with Delay Terms

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources