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Instantaneous blow-up of solutions to a class of hyperbolic inequalities. (English) Zbl 1024.35081

Summary: We prove instantaneous blow-up of nonnegative solutions for a class of semilinear hyperbolic inequalities with first order terms and singular coefficients. The present approach relies on a suitable choice of the functions used to test the differential inequalities.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35R45 Partial differential inequalities and systems of partial differential inequalities
35L15 Initial value problems for second-order hyperbolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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