Solutions of the wave equation with localized energy

DOI10.1002/cpa.3160220605zbMath0209.40402OpenAlexW2118766761MaRDI QIDQ5611236

J. V. Ralston

Publication date: 1969

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160220605

Mathematics Subject Classification ID

Wave equation (35L05)

Related Items

Stabilization of a semilinear wave equation with delay, Optimal decay rate for the wave equation on a square with constant damping on a strip, No events on closed causal curves, Local energy decay and smoothing effect for the damped Schrödinger equation, The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds, Decay for solutions of the wave equation on Kerr exterior spacetimes. III: The full subextremalcase \(|a| < M\)., Decay of solutions of the wave equation outside rough surfaces, Morawetz estimates for the wave equation at low frequency, Mathematics of Hybrid Imaging: A Brief Review, Local energy decay for hyperbolic systems in exterior domains, Decay of solutions of the wave equation in the exterior of several convex bodies, Exact controllability for a model of a multidimensional flexible structure, Smoothing effect for regularized Schrödinger equation on compact manifolds, Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations, Unique continuation from infinity in asymptotically anti-de Sitter spacetimes, Energy decay in a wave guide with dissipation at infinity, Total energy decay for the wave equation in exterior domains with a dissipation near infinity, Asymptotic Stability for the Damped Schrödinger Equation on Noncompact Riemannian Manifolds and Exterior Domains, Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes, Energy flow: Wave motion and geometrical optics, Energy decay for a locally undamped wave equation, Local energy decay for the wave equation on the exterior of two balls or convex bodies, Attractors for semilinear wave equations with localized damping and external forces, Normally hyperbolic trapping on asymptotically stationary spacetimes, Finite codimensional controllability and optimal control problems with endpoint state constraints, The Kato smoothing effect for regularized Schrödinger equations in exterior domains, Local energy decay of the wave equation in an exterior problem and without resonance in the neighborhood of the real line, Attractors for wave equations with degenerate memory, Formation of singularities of limiting amplitude in a density stratified fluid disturbed by an extended monochromatic forcing, Sharp exponential decay rates for anisotropically damped waves, A system of Schrödinger equations in a wave guide, Integrated Local Energy Decay for the Damped Wave Equation on Stationary Space-Times, A note on local energy decay results for wave equations with a potential, Hidden symmetries and decay for the wave equation on the Kerr spacetime, The Strauss Conjecture on Asymptotically Flat Space-Times, Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach, Global existence for a coupled wave system related to the Strauss conjecture, Pointwise decay for the wave equation on nonstationary spacetimes, L2-blowup estimates of the wave equation and its application to local energy decay, Decay of the local energy for the charged Klein-Gordon equation in the exterior de Sitter-Reissner-Nordström spacetime, Energy decay for a localized degenerate hyperbolic equation in an exterior domain, The effect of metric behavior at spatial infinity on pointwise wave decay in the asymptotically flat stationary setting, Sharp polynomial decay rates for the damped wave equation with Hölder-like damping, Local energy decay for the damped Klein-Gordon equation in exterior domain, On the decay of solutions to the 2D Neumann exterior problem for the wave equation., Exponential stability for the wave model with localized memory in a past history framework, Singularities of the scattering kernel for trapping obstacles, A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds, Internal control of the Schrödinger equation, A local energy estimate for wave equations on metrics asymptotically close to Kerr, Scattering of waves by periodically moving bodies, Local energy decay for Lipschitz wavespeeds, Exponential decay for the Schrödinger equation on a dissipative waveguide, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, LOCAL DECAY FOR THE DAMPED WAVE EQUATION IN THE ENERGY SPACE, Resolvent estimates and local energy decay for hyperbolic equations, Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric, Local energy decay for the wave equation with a nonlinear time-dependent damping, Diffractive propagation on conic manifolds, Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain, Unified approach to stabilization of waves on compact surfaces by simultaneous interior and boundary feedbacks of unrestricted growth, Mathematical study of scattering resonances, Local energy decay for the damped wave equation, The trapping effect on degenerate horizons, Solutions of the wave equation which decay with respect to time at a prescribed rate, Stabilization of the wave equation in an exterior domain, Local energy decay for a class of nonstar-shaped bodies, Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping, Geometrical optics and the corner problem, Stabilization of Schrödinger equation in exterior domains, Hyperbolic trapped rays and global existence of quasilinear wave equations, Strichartz estimates on Schwarzschild black hole backgrounds, Contrôle et stabilisation d'ondes électromagnétiques, Some remarks on the local energy decay of solutions of the initial- boundary value problem for the wave equation in unbounded domains, A priori bounds for solutions of the Dirichlet problem for [Delta + lambda sup(2) n(x)u = f(x,lambda) on an exterior domain], Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions, The Strauss conjecture on Kerr black hole backgrounds, Propagation, reflection, and diffraction of singularities of solutions to wave equations, An alternative proof of global existence for nonlinear wave equations in an exterior domain, A note on decay rates of the local energy for wave equations with Lipschitz wavespeeds, Local energy decay in linear elastodynamics, Control from an interior hypersurface, Wave propagation on microstate geometries, Singular internal stabilization of the wave equation, Asymptotic properties of linear field equations in anti-De Sitter space, Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation, Stabilization rates for the damped wave equation with Hölder-regular damping, Weighted energy estimates for wave equations in exterior domains, Unnamed Item, Asymptotic boundary observability for the wave equation on one side of a planar triangle, Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II, On the interaction of metric trapping and a boundary, Asymptotic behaviour of solutions for the wave equation with an effective dissipation around the boundary, Localized Energy Estimates for Wave Equations on (1+4)-dimensional Myers--Perry Space-times, Note on the distribution of poles of the scattering matrix, Wave decay on manifolds with bounded Ricci tensor, and related estimates, Operator-valued \((L^p, L^q)\) Fourier multipliers and stability theory for evolution equations, The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds, The stable trapping phenomenon for black strings and black rings and its obstructions on the decay of linear waves

Cites Work

• Asymptotic Expansions