Critical exponent and critical blow-up for quasilinear parabolic equations
type: Item
instance of: scholarly article
title: Critical exponent and critical blow-up for quasilinear parabolic equations
zbMATH Open document ID: 0880.35057
DOI: 10.1007/BF02937331
author: K. Mochizuki
author: Ryuichi Suzuki
published in: Israel Journal of Mathematics
publication date: 1998-01-28T00:00:00Z
review text: This paper deals with nonlinear parabolic equations of the following type \[ u_t-\Delta u^m= u^p\quad\text{in }D\times (0,T), \] \[ u(x,t)= 0\quad\text{on }\partial D\times (0,T),\quad u(x,0)= u_0(x)\geq 0. \] Here \(D\) is either \(\mathbb{R}^N\) or an exterior domain. It is shown that for certain ranges of \(p\) and \(m\) no nontrivial solution exists for all times \(t>0\). If a solution ceases to exist, it blows up. The authors use a variant of the method of Fourier coefficients which is common in this type of studies. They obtain interesting estimates for the solutions.
reviewed by: Catherine Bandle
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 1033782
zbMATH Keywords: unbounded domains
zbMATH Keywords: method of Fourier coefficients
MaRDI profile type: Publication
cites work: On the Existence and Nonexistence of Global Solutions of Reaction-Diffusion Equations in Sectorial Domains
cites work: Positivity versus localization in degenerate diffusion equations
cites work: Q5547841
cites work: Blow-up for quasilinear heat equations with critical Fujita's exponents
cites work: Q3661987
cites work: Non existence of global solutions of parabolic equation in conical domains
cites work: On nonexistence of global solutions of some semilinear parabolic differential equations
cites work: On blow-up of solutions for quasilinear degenerate parabolic equations
cites work: Q4344331
cites work: Q5562267
cites work: The Role of Critical Exponents in Blowup Theorems
cites work: A blowup result for the critical exponent in cones
cites work: Some existence and nonexistence theorems for solutions of degenerate parabolic equations
cites work: Existence and nonexistence of global solutions to fast diffusions with source
cites work: Blow-up sets and asymptotic behavior of interfaces for quasilinear degenerate parabolic equations in \(\mathbb{R}^ N\)
cites work: Q3269387
cites work: DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
cites work: Critical blow-up for quasilinear parabolic equations in exterior domains
cites work: Existence and non-existence of global solutions for a semilinear heat equation
full work available at URL: https://doi.org/10.1007/bf02937331
OpenAlex ID: W2079059539
description: scientific article; zbMATH DE number 1033782