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Global existence and blow-up for wave equations with weighted nonlinear terms in one space dimension. (English) Zbl 1288.35354

Summary: We consider the initial value problem for wave equations with weighted nonlinear terms in one space dimension. Under the assumption that the initial data and nonlinearity are odd functions, we are able to show global existence of small amplitude solutions. We also prove that symmetric assumptions on the initial data are necessary to obtain the global solution, by showing a blow-up result.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B44 Blow-up in context of PDEs
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