Blow-up in Nonlinear Heat Equations

The Blow-up Rate Estimates for a System of Heat Equations with Nonlinear Boundary Conditions

This paper deals with the blow-up properties of positive solutions to a system of two heat equations ut = ∆u, vt = ∆v in BR× (0, T ) with Neumann boundary conditions ∂u ∂η = e vp , ∂v ∂η = e uq on ∂BR × (0, T ), where p, q > 1, BR is a ball in Rn, η is the outward normal. The upper bounds of blow-up rate estimates were obtained. It is also proved that the blow-up occurs only on the boundary.

BLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

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...

v 1 2 1 Ju n 19 93 Universality in Blow - Up for Nonlinear Heat Equations

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer k, we construct a set of codimension 2k in the space of initial data giving rise to solutions that blow-up according to the given profile.

Blow-up at space infinity for nonlinear heat equations

A note on blow-up in parabolic equations with local and localized sources

‎This note deals with the systems of parabolic equations with local and localized sources involving $n$ components‎. ‎We obtained the exponent regions‎, ‎where $kin {1,2,cdots,n}$ components may blow up simultaneously while the other $(n-k)$ ones still remain bounded under suitable initial data‎. ‎It is proved that different initial data can lead to different blow-up phenomena even in the same ...