Blow-Up of Solutions for a Class Quasilinear Wave Equation with Nonlinearity Variable Exponents

Abstract

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 − Δ u t t 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 (Appl Anal. 2017; 96(9): 1509-1515).

The Blow-Up of the Local Energy Solution to the Wave Equation with a Nontrivial Boundary Condition

“…This article has already addressed the issue of system solution blow-up under positive initial energy, and we further estimate the upper and lower bounds of the solution blow-up time. Considerable progress has been made in demonstrating to the wave equation, especially in cases where the initial energy is negative, the conclusions about blow-up solution have been proved [8][9][10][11][12][13][14][15]. Meanwhile, many similar results also have been found when the initial energy is positive (see [16][17][18][19]).…”