Blow-up of solutions for a class quasilinear wave equation with nonlinearity variable exponents
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 [\textit{S. A. Messaoudi} and \textit{A. A. Talahmeh}, Appl. Anal. 96, No. 9, 1509--1515 (2017; Zbl 1382.35055)].
scientific article; zbMATH DE number 7365474
scientific article