Qualitative behavior of dissipative wave equations on bounded domains

DOI10.1007/BF00251857zbMath0335.35062OpenAlexW1967476058MaRDI QIDQ1229364

Jeffrey Rauch

Publication date: 1976

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251857

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (18)

Energy decay for the wave equation with a degenerate dissipative term ⋮ Convergence of the wave equation damped on the interior to the one damped on the boundary ⋮ The rate at which energy decays in a damped String ⋮ Long-time behavior of a coupled heat-wave system arising in fluid-structure interaction ⋮ Global stability of steady transonic Euler shocks in quasi-one-dimensional nozzles ⋮ Well-posedness of optimal actuator and damping design with application to quadratic performance measures ⋮ Dynamic stability of transonic shock solutions for one-dimensional Euler equations with external forcing ⋮ Exponential decay of solutions of damped nonlinear hyperbolic equations ⋮ Stability of transonic shock solutions for one-dimensional Euler-Poisson equations ⋮ Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: A sharp result ⋮ Some spatial decay estimates in continuum dynamics ⋮ Regularity of invariant sets in variable internal damped wave equations ⋮ On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations ⋮ Dynamic version of Saint-Venant's principle-historical account and recent results ⋮ A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam ⋮ Generic transversality property for a class of wave equations with variable damping ⋮ Dissipative operators with finite dimensional damping ⋮ Global in time stability of steady shocks in nozzles

Cites Work

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• Local decay of solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions in exterior domains
• Decay of solutions to nondissipative hyperbolic systems on compact manifolds

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