Asymptotic behavior of solutions to the semilinear wave equation with time-dependent damping
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Publication:763998
DOI10.3836/tjm/1327931389zbMath1242.35174OpenAlexW2093294756MaRDI QIDQ763998
Publication date: 3 April 2012
Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3836/tjm/1327931389
Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Damped wave equation in the subcritical case
- Wave equations with time-dependent dissipation. I: Non-effective dissipation
- Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption
- Wave equations with time-dependent dissipation. II: Effective dissipation
- Damped wave equation with super critical nonlinearities.
- On the critical nonlinear damped wave equation with large initial data
- Asymptotic behaviors of solutions for time dependent damped wave equations
- Scattering theory for wave equations with dissipative terms
- Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
- \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
- Diffusion phenomenon for linear dissipative wave equations in an exterior domain
- Large time behavior and \(L^{p}\)-\(L^{q}\) estimate of solutions of 2-dimensional nonlinear damped wave equations
- \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
- On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term
- Asymptotic behavior for abstract wave equations with decaying dissipation
- A blow up result for a nonlinear wave equation with damping and vanishing initial energy in \(\mathbb R^N\)
- Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption
- Global asymptotics for the damped wave equation with absorption in higher dimensional space
- A blow-up result for a nonlinear wave equation with damping: The critical case
- Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential
- Diffusion phenomenon for second order linear evolution equations
- Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
- Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term
- Critical exponent for a nonlinear wave equation with damping
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