具阻尼项的Boussinesq型方程的长时间行为

Abstract

Abstract:

In this paper, we study the long time behavior of the solution of the initial boundary value problem of Boussinesq type equation with damping term:u_tt-Δu+Δ²u-Δu_t-Δg(u)=f(x). The main result is that the existence of global attractor of the infinite dimensional dynamical system and the existence of the global attractor and the Hausdorff dimension of the attractor in the phase space E=V₂×H are proved by the method of semi group decomposition, The abstract ondition of nonlinear term g(u) is verified and given a concrete example.

Key words: Boussinesq type equation, Initial boundary value problem, Infinite dimensional dynamical system, Global attractor, Hausdorff dimension

CLC Number:

O175.29

Geng Fan, Li Ruizhai, Ge Xiangyu. Long Time Behavior of Boussinesq Type Equation with Damping Term[J].Acta mathematica scientia,Series A, 2016, 36(6): 1196-1210.

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Long Time Behavior of Boussinesq Type Equation with Damping Term

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