Global nonexistence for a quasilinear evolution equation with a generalized Lewis function
type: Item
instance of: scholarly article
title: Global nonexistence for a quasilinear evolution equation with a generalized Lewis function
zbMATH Open document ID: 1065.35163
DOI: 10.4171/ZAA/1236
author: Yong Zhou
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2005-07-06T00:00:00Z
review text: Summary: We consider the following quasilinear parabolic equation \[ a(x,t)u_t-\text{div}\bigl(|\nabla u|^{m-2}\nabla u\bigr)=f(u), \] where \(a(x,t)\geq 0\) is a generalized Lewis function. The main result is that the solution blows up in finite time if the initial datum \(u(x,0)\) possesses suitable positive energy. Moreover, we have a precise estimate for the lifespan of the solution in this case. Blow up of solutions with vanishing initial energy is considered, too.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2186776
zbMATH Keywords: estimate for the lifespan
zbMATH Keywords: Blow up
MaRDI profile type: Publication
cites work: The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
cites work: Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
cites work: Q4056957
cites work: Saddle points and instability of nonlinear hyperbolic equations
cites work: Global nonexistence for abstract evolution equations with positive initial energy
cites work: The reaction-diffusion equation with Lewis function and critical Sobolev exponent
cites work: Global nonexistence theorems for a class of evolution equations with dissipation
cites work: Q4825378
full work available at URL: https://doi.org/10.4171/zaa/1236
OpenAlex ID: W1993792976
description: scientific article; zbMATH DE number 2186776