Theory of damped wave models with integrable and decaying in time speed of propagation

DOI10.1142/S0219891616500132zbMath1398.35135MaRDI QIDQ2818346

Marcelo Rempel Ebert, Michael Reissig

Publication date: 7 September 2016

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemdissipationdecay estimateWKB analysiseffective dissipationdamped wave modeltime-dependent speed

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (13)

Global in time existence of self-interacting scalar field in de Sitter spacetimes ⋮ Critical exponent for a class of semilinear damped wave equations with decaying in time propagation speed ⋮ Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity ⋮ Critical exponent of Fujita type for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime ⋮ Scale-invariant semilinear damped wave models with mass term and integrable in time speed of propagation. ⋮ Integral Transform Approach to Time-Dependent Partial Differential Equations ⋮ Classification of asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients: effective damping case ⋮ Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime ⋮ Convergence to nonlinear diffusion waves for solutions of \(p\)-system with time-dependent damping ⋮ Time-dependent propagation speed vs strong damping for degenerate linear hyperbolic equations ⋮ Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients ⋮ Smoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operators ⋮ Diffusion phenomenon for abstract linear wave equations with time decaying coefficients of propagation and dissipation

Cites Work

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• Global existence of the scalar field in de Sitter spacetime
• On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions
• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• \(C^m\)-theory of damped wave equations with stabilisation
• A class of dissipative wave equations with time-dependent speed and damping
• The Interplay Between Time-dependent Speed of Propagation and Dissipation in Wave Models

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