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Instability of standing waves for Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions. (English) Zbl 1068.35066

Summary: This paper is concerned with the standing wave for Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions. The existence of standing wave with the ground state is established by applying an intricate variational argument and the instability of the standing wave is shown by applying Pagne and Sattinger’s potential well argument and Levine’s concavity method.

MSC:

35L55 Higher-order hyperbolic systems
35B35 Stability in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35R25 Ill-posed problems for PDEs
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