A Blowup Problem of Reaction Diffusion Equation Related to the Diffusion Induced Blowup Phenomenon

2003/07/31 by Chu-Pin Lo, Lo, Chu-Pin
Mathematics · #35K10 #35K15 #35K20 #35K40 #35K45 #35K50 #35K55 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35K10 #msc:35K15 #msc:35K20 #msc:35K40 #msc:35K45 #msc:35K50 #msc:35K55

paper · pdf · doi:10.48550/arxiv.math/0307397

arxiv created 2003/07/31 · arxiv updated 2009/12/01

Abstract

This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients of this equation are presented. Applying the results allows one to construct some reaction diffusion systems with the so-called diffusion-induced blowup phenomenon, particularly in the case of equal diffusion rates.

Related

• Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems
• Blow-up phenomena for a reaction diffusion equation with special diffusion process
• On Blow-up of A Reaction Diffusion System Coupled in Both Equations and Boundary Conditions
• Blow-up in reaction-diffusion systems under Robin boundary conditions
• Preventing Finite-Time Blowup in a Constrained Potential for Reaction-Diffusion Equations