On diffusion phenomena for the linear wave equation with space-dependent damping
From MaRDI portal
Publication:5179045
DOI10.1142/S0219891614500246zbMath1312.35026arXiv1309.3377WikidataQ115245221 ScholiaQ115245221MaRDI QIDQ5179045
Publication date: 19 March 2015
Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1309.3377
Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)
Related Items (30)
Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data ⋮ Remarks on the asymptotic behavior of the solution to damped wave equations ⋮ The lifespan of solutions to semilinear damped wave equations in one space dimension ⋮ Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain ⋮ Energy decay in a wave guide with dissipation at infinity ⋮ Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients ⋮ Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms ⋮ A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ Asymptotic expansion of solutions to the wave equation with space-dependent damping ⋮ Lifespan estimates for semilinear wave equations with space dependent damping and potential ⋮ Asymptotic behavior for wave equations with space-dependent damping in a weighted energy class ⋮ Decay property of solutions to the wave equation with space‐dependent damping, absorbing nonlinearity, and polynomially decaying data ⋮ Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain ⋮ Blow-up and lifespan estimates for solutions to the weakly coupled system of nonlinear damped wave equations outside a ball ⋮ Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data ⋮ Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution ⋮ Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation ⋮ Critical exponent for the semilinear wave equations with a damping increasing in the far field ⋮ Finite time blow-up for damped wave equations with space-time dependent potential and nonlinear memory ⋮ Critical exponent for semi-linear wave equations with double damping terms in exterior domains ⋮ Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms ⋮ Diffusion phenomenon for indirectly damped hyperbolic systems coupled by velocities in exterior domains ⋮ Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations ⋮ Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data ⋮ Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity ⋮ Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain ⋮ On a strongly damped semilinear wave equation with time-varying source and singular dissipation ⋮ Blow-up rates for a higher-order semilinear parabolic equation with nonlinear memory term ⋮ Sharp time decay rates on a hyperbolic plate model under effects of an intermediate damping with a time-dependent coefficient
Cites Work
- Unnamed Item
- Nonlinear dissipative wave equations with space-time dependent potential
- Wave equations with time-dependent dissipation. II: Effective dissipation
- On the critical nonlinear damped wave equation with large initial data
- Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients
- Scattering theory for wave equations with dissipative terms
- The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
- \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
- An optimal estimate for the difference of solutions of two abstract evolution equations.
- Global existence of solutions for semilinear damped wave equations in \(\mathbb R^N\) with noncompactly supported initial data
- 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
- Wave equations with strong damping in Hilbert spaces
- Optimal decay rate of the energy for wave equations with critical potential
- Diffusion phenomenon in Hilbert spaces and applications
- Diffusion phenomena for the wave equation with structural damping in the \(L^p-L^q\) framework
- 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
- Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation
- Diffusion phenomenon for second order linear evolution equations
- Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term
- Damped wave equation with a critical nonlinearity
- On the diffusion phenomenon of quasilinear hyperbolic waves
- Critical exponent for a nonlinear wave equation with damping
This page was built for publication: On diffusion phenomena for the linear wave equation with space-dependent damping