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http://dx.doi.org/10.4134/JKMS.j200202

BLOW-UP OF SOLUTIONS FOR WAVE EQUATIONS WITH STRONG DAMPING AND VARIABLE-EXPONENT NONLINEARITY  

Park, Sun-Hye (Office for Education Accreditation Pusan National University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.3, 2021 , pp. 633-642 More about this Journal
Abstract
In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity utt(x, t) - ∆u(x, t) - ∆ut(x, t) = |u(x, t)|p(x)-2u(x, t), where the exponent p(·) 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;
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