Regularity of higher energies of wave equation with nonlinear localized damping and a nonlinear source

DOI10.1016/j.na.2008.02.069zbMath1149.35060OpenAlexW2057804709MaRDI QIDQ943716

Daniel Toundykov, Irena Lasiecka

Publication date: 10 September 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.02.069

zbMATH Keywords

stabilityuniform boundednessstrong solutionsloss of dissipativitynonlinear characteristics of dissipation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Second-order nonlinear hyperbolic equations (35L70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• Optimal decay rates for solutions of a nonlinear wave equation with localized nonlinear dissipation of unrestricted growth and critical exponent source terms under mixed boundary conditions
• Nonlinear evolution equations - global behavior of solutions
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Existence for a nonlinear wave equation with damping and source terms.
• Analysis and control of nonlinear infinite dimensional systems
• Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms
• Mathematical Control Theory of Coupled PDEs
• Optimality of Energy Estimates for the Wave Equation with Nonlinear Boundary Velocity Feedbacks
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
• Equivalent Norms for Sobolev Spaces

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