Resonance-type behaviour in a system of nonlinear wave equations

DOI10.1016/0022-0396(89)90157-5zbMath0685.35073OpenAlexW2035457112MaRDI QIDQ1826037

M. Kovalyov

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-0396(89)90157-5

zbMATH Keywords

global existencesmall initial values

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order nonlinear hyperbolic equations (35L70) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (11)

An elementary proof of global or almost global existence for quasi-linear wave equations ⋮ Global existence for a system of multiple-speed wave equations violating the null condition ⋮ On global small amplitude solutions to systems of cubic nonlinear Klein--Gordon equations with different mass terms in one space dimension ⋮ Lifespan for radially symmetric solutions to systems of semilinear wave equations with multiple speeds ⋮ Global existence for systems of wave equations with nonresonant nonlinearities and null forms ⋮ Global existence of null-form wave equations on small asymptotically Euclidean manifolds ⋮ An alternative proof of global existence for nonlinear wave equations in an exterior domain ⋮ Small data blowup for systems of semilinear wave equations with different propagation speeds in three space dimensions ⋮ Remarks on energy approach for global existence of some one-dimension quasilinear hyperbolic systems ⋮ On nonlinear elastic waves in 2-D ⋮ Systems of semilinear wave equations with multiple speeds in two space dimensions and a weaker null condition

Cites Work

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• Long‐time behaviour of solutions of a system of nonlinear wave equations
• Nonlinear waves in friedman-robertson-walker space-times
• Blow-up for quasi-linear wave equations in three space dimensions
• Compressible and incompressible fluids
• Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions
• Global existence for nonlinear wave equations
• Global, small amplitude solutions to nonlinear evolution equations

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