Local solutions for a coupled system of Kirchhoff type

DOI10.1016/j.na.2011.07.030zbMath1230.35055OpenAlexW2057055424MaRDI QIDQ642574

Aldo T. Lourêdo, Manuel Milla Miranda

Publication date: 27 October 2011

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.2011.07.030

zbMATH Keywords

Galerkin methodnonlinear dissipationlocal solutions

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Boundary value problems for nonlinear higher-order PDEs (35G30) Wave equation (35L05)

Related Items

Existence of multi-bump solutions for a nonlinear Kirchhoff-type system ⋮ On a nonlinear degenerate evolution equation with nonlinear boundary damping ⋮ Existence, uniqueness, and exponential stability for the Kirchhoff equation in whole hyperbolic space ⋮ On a nonlinear wave equation with boundary damping ⋮ Unnamed Item ⋮ Well-posedness and stability for Kirchhoff equation with non-porous acoustic boundary conditions ⋮ Nonlinear boundary stabilization for Timoshenko beam system

Cites Work

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• A direct method for the boundary stabilization of the wave equation
• Every superposition operator mapping one Sobolev space into another is continuous
• Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
• Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping
• Existence and boundary stabilization of solutions for the kirchhoff equation
• Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation
• Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation