Decay estimates of solutions for the wave equations with strong damping terms in unbounded domains

DOI10.1002/mma.235zbMath0983.35022OpenAlexW1983430302MaRDI QIDQ2747414

Ryo Ikehata

Publication date: 9 April 2002

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.235

zbMATH Keywords

energy decayexterior problemweighted initial dataMorawetz method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for higher-order hyperbolic equations (35L35)

Related Items (15)

A generalized finite element method for the strongly damped wave equation with rapidly varying data ⋮ A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain ⋮ Linear wave equations with time-dependent propagation speed and strong damping ⋮ Some remarks on the asymptotic profiles of solutions for strongly damped wave equations on the 1-D half space ⋮ Finite time blow-up for wave equations with strong damping in an exterior domain ⋮ Global existence of weak solutions for two-dimensional semilinear wave equations with strong damping in an exterior domain ⋮ Asymptotic profiles of solutions for structural damped wave equations ⋮ Optimal leading term of solutions to wave equations with strong damping terms ⋮ Asymptotic profiles for wave equations with strong damping ⋮ Asymptotic periodicity for strongly damped wave equations ⋮ Local and global smoothing effects for some linear hyperbolic equations with a strong dissipation ⋮ The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case ⋮ Critical exponent for semi-linear wave equations with double damping terms in exterior domains ⋮ Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients ⋮ Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

Cites Work

• On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity
• The global existence of small amplitude solutions to the nonlinear acoustic wave equation
• The decay of solutions of the exterior initial-boundary value problem for the wave equation
• Variational problems related to self-similar solutions of the heat equation
• Unnamed Item

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