Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping

DOI10.1063/1.3544046zbMath1314.35177OpenAlexW2056838366MaRDI QIDQ5256233

Zai-Yun Zhang, Xiu-Jin Miao, Yue-Zhong Chen, Zhen-Hai Liu

Publication date: 22 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3544046

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (14)

Asymptotic behavior for a weak viscoelastic wave equations with a dynamic boundary and time varying delay term ⋮ General decay of energy to a nonlinear viscoelastic two-dimensional beam ⋮ Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited ⋮ A new blow-up criterion for the \(N - abc\) family of Camassa-Holm type equation with both dissipation and dispersion ⋮ Existence and regularity of global solutions to a Cauchy problem for a square phase-field crystal model ⋮ Wave breaking and global existence for the generalized periodic Camassa-Holm equation with the weak dissipation ⋮ Homotopy Padé method for solving second-order one-dimensional telegraph equation ⋮ Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback ⋮ Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion ⋮ Unstable oscillating systems with hysteresis: problems of stabilization and control ⋮ General energy decay of solutions for a weakly dissipative Kirchhoff equation with nonlinear boundary damping ⋮ Unnamed Item ⋮ Optimal control of a viscous generalized \(\theta\)-type dispersive equation with weak dissipation ⋮ Global existence and general decay for a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: A sharp result
• Energy decay and exact controllability for the Petrovsky equation in a bounded domain
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping
• A direct method for the boundary stabilization of the wave equation
• Stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions
• Uniform stabilization of a nonlinear beam by nonlinear boundary feedback
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Wave equation on a bounded domain with boundary dissipation: An operator approach
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain
• On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions
• A note on the boundary stabilization of a compactly coupled system of wave equations
• Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
• Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term
• Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
• Global existence for the wave equation with nonlinear boundary damping and source terms
• Une nouvelle approche pour la stabilisation des systèmes distribués non dissipatifs
• Asymptotic stability of the wave equation on compact surfaces and locally distributed damping-A sharp result
• Uniform Stabilization of the Wave Equation by Nonlinear Boundary Feedback
• Note on Boundary Stabilization of Wave Equations
• A Note on the Boundary Stabilization of the Wave Equation
• Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
• Control and Stabilization for the Wave Equation in a Bounded Domain
• Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term
• A New Approach of Stabilization of Nondissipative Distributed Systems
• Compactons: Solitons with finite wavelength
• Asymptotic Behaviour of Solutions of the One-Dimensional Wave Equation with a Nonlinear Boundary Stabilizer
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION

This page was built for publication: Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping