Existence and nonexistence of time-global solutions to damped wave equation on half-line
type: Item
instance of: scholarly article
title: Existence and nonexistence of time-global solutions to damped wave equation on half-line
zbMATH Open document ID: 1079.35014
author: Kenji Nishihara
author: Huijiang Zhao
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-06-13T00:00:00Z
review text: The authors compare the existence and the blowup properties of solutions to the semilinear heat equation \(\phi_t-\phi_{xx}=f(\phi)\) and the semilinear damped wave equation \(u_{tt}+u_t-u_{xx}=f(u)\), both with \(f(u)\sim | u| ^\rho\), posed in the half-space \(x,t\in (0,\infty)\), supplemented with the Dirichlet boundary conditions, and with suitable initial data. In particular, in the case of the first equation and for \(1<\rho\leq \rho_c=2\), they derive estimates (from above and below) of the blowup time. Next, an analogous result is shown for the damped wave equation.
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 2175668
zbMATH Keywords: semilinear heat equation
zbMATH Keywords: semilinear damped wave equation
zbMATH Keywords: Dirichlet boundary conditions
MaRDI profile type: Publication
full work available at URL: j.na.2005.01.025
OpenAlex ID: W2047419680
cites work: An optimal estimate for the difference of solutions of two abstract evolution equations.
cites work: Q4001895
cites work: The role of critical exponents in blow-up theorems: The sequel
cites work: Stability of travelling waves for a damped hyperbolic equation
cites work: Scaling variables and asymptotic expansions in damped wave equations
cites work: On the diffusion phenomenon of quasilinear hyperbolic waves
cites work: On nonexistence of global solutions of some semilinear parabolic differential equations
cites work: Damped wave equation with super critical nonlinearities.
cites work: Damped wave equation with a critical nonlinearity
cites work: Damped wave equation in the subcritical case
cites work: Large time behavior and \(L^{p}\)-\(L^{q}\) estimate of solutions of 2-dimensional nonlinear damped wave equations
cites work: Critical exponent for semilinear damped wave equations in the \(N\)-dimensional half space.
cites work: New decay estimates for linear damped wave equations and its application to nonlinear problem
cites work: Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
cites work: Diffusion phenomenon for second order linear evolution equations
cites work: Critical exponents for semilinear dissipative wave equations in \({\mathbb{R}}^N\)
cites work: On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term
cites work: Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
cites work: The Role of Critical Exponents in Blowup Theorems
cites work: A blowup result for the critical exponent in cones
cites work: The value of the critical exponent for reaction-diffusion equations in cones
cites work: Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
cites work: The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
cites work: On the asymptotic behavior of solutions of semi-linear wave equations
cites work: Blow-up of solutions of semilinear parabolic differential equations
cites work: On the critical exponent for reaction-diffusion equations
cites work: \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
cites work: Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
cites work: \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
cites work: Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption
cites work: Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations
cites work: Global Solvability and Lp Decay for the Semilinear Dissipative Wave Equations in Four and Five Dimensions
cites work: Critical exponent for a nonlinear wave equation with damping
cites work: Existence and non-existence of global solutions for a semilinear heat equation
cites work: A blow-up result for a nonlinear wave equation with damping: the critical case
DOI: 10.1016/J.NA.2005.01.025
description: scientific article; zbMATH DE number 2175668