Existence, decay and blow-up results for a plate viscoelastic equation with variable-exponent logarithmic terms

Abstract

In the present study, we investigate the solution behavior for a class of fourth-order viscoelastic equation with logarithmic terms with variable-exponent nonlinearities. First, we prove the global existence of solutions, and next, by constructing suitable auxiliary functionals, the general decay of solutions has been proved when the exponents satisfy appropriate conditions. Finally, under suitable conditions on data, we establish the finite time blow-up of solutions with positive initial energy. Our results extend and improve many results in the literature.