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 Blow-up of solutions for wave equations with strong damping and variable-exponent nonlinearity J. Korean Math. Soc.Published online September 22, 2020 Sun-Hye Park Pusan National University Abstract : In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity $$u_{tt}(x,t) - \Delta u (x,t) - \Delta u_t (x,t) = |u(x,t)|^{p(x)-2} u(x,t) ,$$ where the exponent $p(\cdot)$ of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity. Keywords : wave equation, variable-exponent nonlinearity, finite time blow-up, strong damping MSC numbers : 35L05, 35L70, 35B44 Full-Text :