Blow-up time bounds for a strongly damped wave equation with PINNs validation

Abstract

This work investigates the blow-up behavior of solutions to a strongly damped semilinear wave equation on bounded domains. By imposing specific conditions on the initial data, we derive both lower and upper estimates for the blow-up time as well as the range of the threshold regions for the nonlinear exponents. Furthermore, our theoretical findings are numerically validated using physics-informed neural networks (PINNs).