Oscillatory Phenomena Associated to Semilinear Wave Equations in One Spatial Dimension

DOI10.2307/2000596zbMath0628.35058OpenAlexW4250594292MaRDI QIDQ3764570

Thierry Cazenave, Alain Haraux

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000596

zbMATH Keywords

semilinear wave equationoscillationperiodic boundary conditionsDirichletNeumann

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Partial differential inequalities and systems of partial differential inequalities (35R45) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (14)

Density theorems for almost periodic functions: a Hilbet space approach ⋮ Strong decay for wave equations with nonlinear nonmonotone damping ⋮ Generalized master equations and the telegrapher's equation ⋮ Some oscillatory properties of the wave equation in several space dimensions ⋮ A pointwise oscillation property of semilinear wave equations with time-dependent coefficients ⋮ Remarks on weak stabilization of semilinear wave equations ⋮ Nonlinear effects in the wave equation with a cubic restoring force ⋮ A solvable nonlinear reaction-diffusion model ⋮ Oscillatory behavior of solutions of nonlinear wave equations ⋮ Oscillations of a nonlinearly damped extensible beam ⋮ A class of nonlinear, completely integrable abstract wave equations ⋮ Detailed asymptotics for a convex Hamiltonian system with two degrees of freedom ⋮ Oscillatory properties for semilinear degenerate hyperbolic equations of second order ⋮ A remark on hölder continuity of periodic solutions to some nonlinear wave equations

Cites Work

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• Nonlinear evolution equations - global behavior of solutions
• Non-linear semi-groups
• Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
• Periodic solutions of hamiltonian systems

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