Viscoelastic fourth-order wave equation with logarithmic and variable-exponent nonlinearities: blow-up analysis

In this paper, we study a fourth-order viscoelastic wave equation involving variable-exponent nonlinearities and a logarithmic source term, where the memory kernel is a positive, nonincreasing function, and the variable exponents are measurable functions satisfying certain conditions. By employing the energy method alongside several integral inequality techniques, we establish a finite-time blow-up result for all solutions corresponding to negative initial energy, as well as for a specific class of solutions with positive initial energy.