Time decay of solutions to degenerate Kirchhoff type equation

DOI10.1016/S0362-546X(97)00540-3zbMath0936.35033OpenAlexW2070336585MaRDI QIDQ4266406

Tetsu Mizumachi

Publication date: 30 March 2000

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

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00540-3

zbMATH Keywords

small initial dataglobal existence of solutionsasymptotic profileFourier splitting methodestimates of the rate of decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80)

Related Items (11)

Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping ⋮ Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation ⋮ Global attractor for the Kirchhoff type equation with a strong dissipation ⋮ Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates ⋮ Longtime behavior of the Kirchhoff type equation with strong damping on \(\mathbb{R}^N\) ⋮ Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Time-decay estimates ⋮ On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type ⋮ Stability of attractors for the Kirchhoff wave equation with strong damping and critical nonlinearities ⋮ An attractor for a nonlinear dissipative wave equation of Kirchhoff type ⋮ Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay ⋮ Global attractor for the Kirchhoff type equations with strong nonlinear damping and supercritical nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behaviour for the Kirchhoff equation
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• A class of nonlinear hyperbolic problems with global solutions
• Decay properties of solutions to degenerate wave equations with dissipative terms
• Kirchhoff type equations depending on a small parameter
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Some nonlinear degenerate wave equations
• On classical solutions of a quasilinear hyperbolic equation
• On local strong solutions of a nonlinear partial differential equation
• The initial value problem for a stretched string
• On some quasilinear wave equations with dissipative terms
• ON A CLASS OF QUASILINEAR HYPERBOLIC EQUATIONS
• Non-Linear vibration of an elastic string
• Infinite Systems of Nonlinear Oscillation Equations Related to the String
• On the non-linear vibration problem of the elastic string

This page was built for publication: Time decay of solutions to degenerate Kirchhoff type equation