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Blow-up of solutions for a class quasilinear wave equation with nonlinearity variable exponents. (English) Zbl 1467.35063

Summary: This work deals with the blow-up of solutions for a new class of quasilinear wave equation with variable exponent nonlinearities. To clarify more, we prove in the presence of dispersion term \(-\Delta u_{tt}\) a finite-time blow-up result for the solutions with negative initial energy and also for certain solutions with positive energy. Our results are extension of the recent work [S. A. Messaoudi and A. A. Talahmeh, Appl. Anal. 96, No. 9, 1509–1515 (2017; Zbl 1382.35055)].

MSC:

35B44 Blow-up in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L72 Second-order quasilinear hyperbolic equations

Citations:

Zbl 1382.35055
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