Local existence and blow-up of solutions for the higher-order viscoelastic equation with general source term and variable exponents: Theoretical and numerical results

Abstract

This study explores a higher-order viscoelastic equation characterized by variable exponents. We demonstrate the local existence of weak solutions by imposing appropriate conditions on these variable exponents. Furthermore, we investigate the phenomenon of finite-time blow-up for solutions that begin with positive initial energy. Finally, we give a 2D numerical example for the blow up.