Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
type: Item
instance of: scholarly article
title: Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
zbMATH Open document ID: 1030.35125
DOI: 10.1016/S0022-0396(02)00042-6
author: Zhijian Yang
published in: Journal of Differential Equations
publication date: 2003-03-18T00:00:00Z
review text: The author studies the global existence as well as the exponential decay (as \(t\) tends to \(\infty \)) of weak solutions to the problem \[ u_{tt}+ \Delta^2u + \lambda u_t = \sum_{i=1}^N\frac{\partial}{\partial x_i}\sigma_i u_{x_i} \quad \text{in }\Omega \times (0, \infty), \] \[ u=0, \;\;\frac{\partial u}{\partial n} = 0 \quad \text{on }\partial \Omega \times [0,\infty), \] \[ u(x,0)=u_0(x), \;\;u_t(x,0)=u_1(x), \quad x\in \Omega, \] where \(\lambda \geq 0\) is a constant. Under different assumptions the solutions blow up in finite time.
Mathematics Subject Classification ID: 35L75
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1884235
zbMATH Keywords: exponential decay
zbMATH Keywords: blowup
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
cites work: A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models
cites work: On the Strongly Damped Wave Equation: $u_{tt} - \Delta u - \Delta u_t + f(u) = 0$
cites work: Nonlinear second order equations with applications to partial differential equations
cites work: Existence and non-existence of global solutions for a class of non-linear wave equations
cites work: The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
cites work: Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
cites work: Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
cites work: Q4955159
cites work: Q3324344
description: scientific article; zbMATH DE number 1884235