Scattering for a quasilinear hyperbolic equation of Kirchhoff type

DOI10.1006/jdeq.1997.3372zbMath0895.35067OpenAlexW2013924529MaRDI QIDQ1381624

Taeko Yamazaki

Publication date: 20 September 1998

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1997.3372

zbMATH Keywords

global solvability

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (17)

Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term ⋮ On the convergence of a three-layer semi-discrete scheme for the nonlinear dynamic Kirchhoff string equation ⋮ Global well-posedness of Kirchhoff systems ⋮ Blow up and blow up time for degenerate Kirchhoff-type wave problems involving the fractional Laplacian with arbitrary positive initial energy ⋮ Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation ⋮ Majorant sign of the first order for totally global solvability of a controlled functional operator equation ⋮ On preservation of global solvability of controlled second kind operator equation ⋮ \(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation ⋮ Asymptotic profiles for the Kirchhoff equation ⋮ Necessary condition on the dissipative term for the asymptotically free property of dissipative Kirchhoff equations ⋮ Scattering for one dimensional perturbed Kirchhoff equations ⋮ On the Gevrey well-posedness of the Kirchhoff equation ⋮ Time decay for hyperbolic equations with homogeneous symbols ⋮ One-dimensional Kirchhoff equation ⋮ Global solutions for dissipative Kirchhoff strings with \(m(r)=r^p\) \((p<1)\) ⋮ On the singularly perturbation fractional Kirchhoff equations: critical case ⋮ Non-degeneracy of positive solutions for fractional Kirchhoff problems: high dimensional cases

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behaviour for the Kirchhoff equation
• Asymptotic behaviour as \(t \to +\infty\) of the solutions of linear hyp equations with coefficients discontinuous in time (on a bounded domain)
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• Abstract non linear wave equations
• A class of nonlinear hyperbolic problems with global solutions
• A class of second order quasilinear evolution equations
• Kirchhoff type equations depending on a small parameter
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Some nonlinear degenerate wave equations
• The initial value problem for a stretched string
• On some quasilinear wave equations with dissipative terms
• On solutions to some quasilinear hyperbolic equations with nonlinear inhomogeneous terms
• Mathematical analysis of the nonlinear model for the vibrations of a string
• Nonlinear perturbations of the kirchhoff equation
• On the mildly degenerate Kirchhoff string
• On the Well-Posedness of the Kirchhoff String

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