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Asymptotic behavior for strongly damped wave equations on $\mathbb R^3$ with memory

Xuan-Quang Bui|Duong Toan Nguyen|Trong Luong Vu
대한수학회 (The Korean Mathematical Society)|2024.07|대한수학회지 (Journal of the KMS)|제61권 제4호|pp. 797-836|DOI 10.4134/JKMS.j230536

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참고문헌

키워드

memoryunbounded domainStrongly damped wave equationsexponential attractor
주제분류수학

초록

We consider the following strongly damped wave equation on $\mathbb{R}^3$ with memory $$ u_{tt} - \alpha \Delta u_{t} - \beta \Delta u +\lambda u - \int_{0}^\infty \kappa'( s) \Delta u(t-s)ds+ f(x,u) +g(x,u_t)=h, $$ where a quite general memory kernel and the nonlinearity $f$ exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

Abstract

We consider the following strongly damped wave equation on $\mathbb{R}^3$ with memory $$ u_{tt} - \alpha \Delta u_{t} - \beta \Delta u +\lambda u - \int_{0}^\infty \kappa'( s) \Delta u(t-s)ds+ f(x,u) +g(x,u_t)=h, $$ where a quite general memory kernel and the nonlinearity $f$ exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

참고문헌 (22)

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