具有非线性记忆项的耗散波动方程的整体吸引子

Global Attractor for Damped Wave Equations with Nonlinear Memory

中文关键词:  整体吸引子  非线性记忆项  耗散波动方程.

英文关键词:global attractor  nonlinear memory term  damped wave equation.

中文摘要:

      在一个具有光滑边界的有界区域$\Omega\subset{\Bbb{R}}^{n}$上研究了一类具有非线性记忆项的耗散波动方程$$u_{tt}+\alpha u_{t} -\Delta u - \int_{0}^{t}\mu(t-s)|u(s)|^{\beta} u(s)ds + g(u)=f$$的长时间动力行为.基于时间一致的先验估计方法，在相空间${H_{0}^{1}(\Omega) \times L^{2}(\Omega)}$上证明了上述方程所决定的半群的紧的整体吸引子的存在性.

英文摘要:

      Let $\Omega\subset{\Bbb{R}}^{n}$ be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term $$u_{tt}+\alpha u_{t} -\Delta u - \int_{0}^{t}\mu (t-s)|u(s)|^{\beta} u(s)\d s + g(u)=f.$$ Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space ${H_{0}^{1}(\Omega) \times L^{2}(\Omega)}$.