Blow-up of solutions to fractional quasilinear hyperbolic problem

Abstract

In this paper, we consider blow-up solutions of a nonlinear hyperbolic fractional equation with variable exponents of nonlinearities in the fractional space \(\mathcal {H}_{p(\xi )}^{\alpha }(\Omega )\). To achieve this, we introduce a control function and use energy inequalities to discuss various estimates. In this sense, we address the problem of non-existence of solutions and derive an estimate for the upper bound of the blow-up time. Finally, we provide classical theoretical insights into possible special cases of the results obtained in this study.