Critical exponent for a nonlinear wave equation with damping
type: Item
instance of: scholarly article
title: Critical exponent for a nonlinear wave equation with damping
zbMATH Open document ID: 0994.35028
author: Grozdena Todorova
author: Borislav Yordanov
published in: Journal of Differential Equations
publication date: 2002-09-25T00:00:00Z
review text: The critical exponent for the equation \(u_{tt}+u_t=\Delta u +|u|^p\) in \({\mathbb R}^n\) is found. More precisely, it is shown that if \(p>1+2/n\) then all small data solutions are global while all solutions with \(\int u(0,x) dx>0\), \(\int u_t(0,x) dx>0\) blow up in finite time when \(1<p<1+2/n\). This means that the critical exponent is the same as for the equation \(u_t=\Delta u +|u|^p\). The decay rate of small data global solutions is also studied for \(p>1+2/n\).
reviewed by: Marek Fila
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 1656000
zbMATH Keywords: critical exponent for global existence
zbMATH Keywords: blow-up
zbMATH Keywords: decay rate
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3933
OpenAlex ID: W1966382600
cites work: On certain integral equations related to nonlinear wave equations
cites work: Q3826986
cites work: Global existence for solutions of \(\square u=A| u| ^ p\)
cites work: Q5547841
cites work: Weighted Strichartz estimates and global existence for semilinear wave equations
cites work: Existence in the large for \(cmu=F(u)\) in two space dimensions
cites work: Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
cites work: Blow-up of solutions of nonlinear wave equations in three space dimensions
cites work: Generalized functions. Theory and technique
cites work: Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
cites work: On existence and scattering with minimal regularity for semilinear wave equations
cites work: On the asymptotic behavior of solutions of semi-linear wave equations
cites work: Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
cites work: Q4059363
cites work: Nonexistence of global solutions to semilinear wave equations in high dimensions
cites work: Nonlinear scattering theory at low energy
cites work: Q4858785
DOI: 10.1006/JDEQ.2000.3933
description: scientific article; zbMATH DE number 1656000