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Instability and nonexistence of global solutions to nonlinear wave equations of the form \(Pu_{tt}=-A u+ {\mathfrak F} (u)\). (English) Zbl 0288.35003

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L60 First-order nonlinear hyperbolic equations
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