The exponential stability of the problem of transmission of the wave equation

DOI10.1017/S0004972700031683zbMath0914.35074MaRDI QIDQ4399434

Graham H. Williams, Liu, Wei-Jiu

Publication date: 21 June 1999

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

exponential energy decayDirichlet boundary conditionmultiplier techniquesRobin type boundary conditionpiece-wise constant coefficient

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35)

Related Items (31)

Equivalence between observability at the boundary and stabilization for transmission problem of the wave equation ⋮ Stabilization of a transmission problem with past history and acoustic boundary conditions ⋮ On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients ⋮ Polynomial stability of transmission viscoelastic wave and plate equations on Riemannian manifolds ⋮ Stabilization for transmission wave-plate equations with acoustic/memory boundary conditions ⋮ Exact boundary null controllability for a coupled system of plate equations with variable coefficients ⋮ General decay rate estimates and numerical analysis for a transmission problem with locally distributed nonlinear damping ⋮ The lack of exponential stability for a weakly coupled wave equations through a variable density term ⋮ Exponential stability of the transmission wave equation with a distributed delay term in the boundary damping ⋮ Exponential stabilization of the transmission wave equation with dynamical boundary conditions and a delay term ⋮ Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping ⋮ Uniform decay for a plate equation partially dissipative. ⋮ Uniform decay rate for the transmission wave equations with variable coefficients ⋮ Stabilization of transmission coupled wave and Euler-Bernoulli equations on Riemannian manifolds by nonlinear feedbacks ⋮ Existence and nonexistence of global solutions for nonlinear transmission acousticproblem ⋮ Exponential stability for a transmission problem of a viscoelastic wave equation ⋮ A transmission problem for beams on nonlinear supports ⋮ Stabilization of weakly coupled wave equations through a density term ⋮ Boundary feedback stabilization of the transmission problem of Naghdi's model ⋮ Stabilization of the transmission wave/plate equation with variable coefficients ⋮ Exponential stability for a transmission problem of a nonlinear viscoelastic wave equation ⋮ Unnamed Item ⋮ Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin-Voigt damping ⋮ Uniform stability of transmission of wave-plate equations with source on Riemannian manifold ⋮ Decay rates of energy of the 1D damped original nonlinear wave equation ⋮ The exponential tracking and disturbance rejection for the nonlinear wave equation via boundary control without any geometrical conditions on the domain ⋮ Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping. ⋮ Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control ⋮ NONLINEAR WAVE EQUATIONS WITH NONLINEAR TRANSMISSION ACOUSTIC CONDITION ⋮ Nonlinear boundary stabilization for a transmission problem in elasticity ⋮ Stabilization of the transmission wave equation with variable coefficients and interior delay

Cites Work

• Unnamed Item
• Unnamed Item
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• Semigroups of linear operators and applications to partial differential equations
• Scattering theory for dissipative hyperbolic systems
• Unique continuation for elliptic operators: A geometric-variational approach
• A Note on the Boundary Stabilization of the Wave Equation
• Control and Stabilization for the Wave Equation in a Bounded Domain, Part II
• Control and Stabilization for the Wave Equation, Part III: Domain with Moving Boundary
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Dispersal of waves vanishing on the boundary of an exterior domain
• Decay for solutions of the exterior problem for the wave equation
• Control and Stabilization for the Wave Equation in a Bounded Domain
• Boundary Exact Controllability of Interface Problems with Singularities I: Addition of the Coefficients of Singularities
• Exponential decay of solutions of the wave equation

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