Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation

DOI10.1002/mma.1114zbMath1183.35022OpenAlexW2075409651MaRDI QIDQ3182510

Taeko Yamazaki

Publication date: 9 October 2009

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1114

zbMATH Keywords

singular perturbationKirchhoff equationweak dissipationglobal solutionsdecay estimatesquasilinear hyperbolic equationnonlinear PDE of hyperbolic type

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Second-order nonlinear hyperbolic equations (35L70) Integro-partial differential equations (35R09)

Related Items (8)

Hyperbolic-parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation ⋮ Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates ⋮ Necessary condition on the dissipative term for the asymptotically free property of dissipative Kirchhoff equations ⋮ The hyperbolic-elliptic equation with the nonlocal condition ⋮ Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients ⋮ On the Parabolic Regime of a Hyperbolic Equation with Weak Dissipation: The Coercive Case ⋮ Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay ⋮ Diffusion phenomenon for abstract linear wave equations with time decaying coefficients of propagation and dissipation

Cites Work

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• Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Time-decay estimates
• Hyperbolic--parabolic singular perturbation for mildly degenerate Kirchhoff equations: Global-in-time error estimates
• An optimal estimate for the difference of solutions of two abstract evolution equations.
• Singular limit of some quasilinear wave equations with damping terms
• Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type
• Asymptotic behavior for abstract wave equations with decaying dissipation
• An Optimal Estimate for the Time Singular Limit of an Abstract Wave Equation
• Hyperbolic-parabolic singular perturbations for scalar nonlinearities
• On some quasilinear wave equations with dissipative terms
• On the mildly degenerate Kirchhoff string
• Singular perturbation hyperbolic-parabolic for degenerate nonlinear equations of Kirchhoff type

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