FINITE TIME BLOW-UP FOR THE NONLINEAR FOURTH-ORDER DISPERSIVE-DISSIPATIVE WAVE EQUATION AT HIGH ENERGY LEVEL

DOI10.1142/S0129167X12500607zbMath1267.33016MaRDI QIDQ2885376

Yanbing Yang, Run-Zhang Xu

Publication date: 23 May 2012

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

blow-updissipative termfourth-order wave equationdispersive termarbitrarily positive initial energy

Mathematics Subject Classification ID

Wave equation (35L05) Other wave functions (33E15)

Related Items (11)

On the decay and blow-up of solution for a system of nonlinear viscoelastic plate equations with dissipative terms ⋮ Numerical results for a fourth‐order nonlinear wave equation of Kirchhoff type with a viscoelastic term ⋮ Existence and uniform decay estimates for the fourth order wave equation with nonlinear boundary damping and interior source ⋮ Analysis of finite difference schemes for a fourth-order strongly damped nonlinear wave equations ⋮ Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity ⋮ Global existence and asymptotic behavior of solutions for the double dispersive-dissipative wave equation with nonlinear damping and source terms ⋮ The initial-boundary value problems for a class of sixth order nonlinear wave equation ⋮ Global well-posedness for a class of Kirchhoff-type wave system ⋮ Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity ⋮ Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations ⋮ Global well-posedness and global attractor of fourth order semilinear parabolic equation

Cites Work

• Global existence and uniform decay of solutions for a system of wave equations with dispersive and dissipative terms
• Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms
• Saddle points and instability of nonlinear hyperbolic equations
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global solutions and finite time blow up for damped semilinear wave equations
• Existence and uniform decay for a non-linear viscoelastic equation with strong damping
• A symmetric regularized-long-wave equation
• Solitary-Wave Interactions in Elastic Rods
• Mathematical Models for Elastic Structures
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
• Finite amplitude transverse waves in special incompressible viscoelastic solids

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