耗散Hamiltonian振幅方程在E_1空间的指数吸引子

Exponential Attractor for Dissipative Hamiltonian Amplitude Equation in Space E_1

本文研究了耗散Hamiltonian方程生成的非线性连续半群的性质,通过算子分解和构造紧不变集,得到了在空间E_1中非紧半群S(t)导出的紧的指数吸引于,解决了文献中提出的公开问题。

In this paper,we study the property of nonlinear continuous semigroup S(t)produdced by the Dissipative Hamiltonian Amplitude Equation. By the decomplsition of operators and the constructions of compact positively invariant sets, we obtain the exponential attractor produced by noncompact semigroup S(t). This result solves the open problem in literature[1].