Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms

Chengfei Ai, Huixian Zhu, Guoguang Lin
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引用次数: 2

Abstract

This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.
一类非线性强阻尼Kirchhoff波动方程的近似惯性流形
本文研究了一类具有非线性强阻尼项的Kirchhoff波动方程初边值问题解的长时性。首先,为了证明解的平滑效果,我们有效地利用了由方程主算子生成的半群在相空间中的解析性。然后得到了全局吸引子的正则性,构造了方程的近似惯性流形。最后,我们证明了基尔霍夫波动方程的任意轨迹在大时间后进入近似惯性流形的小邻域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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