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
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