Quasilinear hyperbolic–hyperbolic singular perturbations with nonmonotone nonlinearity

DOI10.1016/S0362-546X(97)00737-2zbMath0929.35095MaRDI QIDQ4238384

Tokio Matsuyama

Publication date: 17 January 2000

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

nonlinear elasticityglobal solutionssmall initial energynon-local coefficients

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80)

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Uniform decay of solution for wave equation of Kirchhoff type with nonlinear boundary damping and memory term ⋮ Uniform decay for the unilateral problem associated to the Kirchhoff type wave equations with nonlinear boundary damping ⋮ On uniform decay of solutions for wave equation of Kirchhoff type with nonlinear boundary damping and memory source term ⋮ On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary ⋮ On coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term

Cites Work

• Stable and unstable sets for evolution of parabolic and hyperbolic type
• Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
• Saddle points and instability of nonlinear hyperbolic equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
• On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms
• Kirchhoff type equations depending on a small parameter
• Singular limit of some quasilinear wave equations with damping terms
• On global solution of nonlinear hyperbolic equations
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Hyperbolic-parabolic singular perturbations for scalar nonlinearities
• Some nonlinear degenerate wave equations
• On the mildly degenerate Kirchhoff string
• Quasilinear parabolic-parabolic singular perturbations
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