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Blow-up of solutions for wave equations with strong damping and variable-exponent nonlinearity

박선혜
대한수학회 (The Korean Mathematical Society)|2021.05|대한수학회지 (Journal of the KMS)|제58권 제3호|pp. 633-642|DOI 10.4134/JKMS.j200202

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참고문헌

키워드

Wave equationstrong dampingvariable-exponent nonlinearityfinite time blow-up
주제분류수학

초록

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.

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.

참고문헌 (28)

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