Blow-up estimates for a semilinear coupled parabolic system

Blow - up behaviors for semilinear parabolic systems coupled in equations and boundary conditions ✩

This paper concerns with blow-up behaviors for semilinear parabolic systems coupled in equations and boundary conditions in half space. We establish the rate estimates for blow-up solutions and prove that the blow-up set is ∂R+ under proper conditions on initial data. Furthermore, for N = 1, more complete conclusions about such two topics are given.  2004 Elsevier Inc. All rights reserved.

To The Memory of My Father ,

This thesis is concerned with the study of the Blow-up phenomena for parabolic problems, which can be defined in a basic way as the inability to continue the solutions up to or after a finite time, the so called blow-up time. Namely, we consider the blow-up location in space and its rate estimates, for special cases of the following types of problems: (i) Dirichlet problems for semilinear equat...

Blow-up at the Boundary for Degenerate Semilinear Parabolic Equations

This paper concerns a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover it is proved that for a large class of initial data blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The ...

Blow-up Estimates for Higher-order Semilinear Parabolic Equations

A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries

We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.