Blowing up and global existence of solutions for some degenerate nonlinear wave equations with some dissipation

DOI10.1016/S0362-546X(97)00183-1zbMath0892.35108MaRDI QIDQ4378915

Kosuke Ono

Publication date: 3 August 1998

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

zbMATH Keywords

decay propertiesKirchhoff stringsequations of Kirchhoff type

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Degenerate hyperbolic equations (35L80)

Related Items (18)

LIFESPAN ESTIMATES FOR SOLUTIONS OF POLYHARMONIC KIRCHHOFF SYSTEMS ⋮ Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations ⋮ Blow-up of solutions to a class of Kirchhoff equations with strong damping and nonlinear dissipation ⋮ Dynamics properties for a viscoelastic Kirchhoff-type equation with nonlinear boundary damping and source terms ⋮ Global nonexistence of solutions for viscoelastic wave equations of Kirchhoff type with high energy ⋮ Initial boundary value problem for a Kirchhoff wave model with strong nonlinear damping ⋮ Global existence, asymptotic behavior and blow up of solutions for a Kirchhoff-type equation with nonlinear boundary delay and source terms ⋮ Existence of solutions of nonlinear extensible beam equations ⋮ On decay and blow-up of solutions for a system of nonlinear wave equations ⋮ General decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping ⋮ Global nonexistence for nonlinear Kirchhoff systems with memory term ⋮ Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation ⋮ Global well-posedness for a class of Kirchhoff-type wave system ⋮ A blow-up result for Kirchhoff-type equations with high energy ⋮ Editorial. Progress in nonlinear Kirchhoff problems ⋮ Lifespan of solutions to a hyperbolic type Kirchhoff equation with arbitrarily high initial energy ⋮ Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping ⋮ Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models

Cites Work

• Saddle points and instability of nonlinear hyperbolic equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Decay of solutions of some nonlinear evolution equations
• Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Infinite-dimensional dynamical systems in mechanics and physics.
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded Fourier coefficients
• On continuity of functions with values in various Banach spaces
• On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation
• Decay properties of solutions of some quasilinear hyperbolic equations with strong damping
• On the mildly degenerate Kirchhoff string
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
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