摘要
研究了一类非线性非局部高阶Kirchhoff型偏微分方程的初边值问题.首先,利用先验估计和Galerkin方法证明了方程在空间H0m+k(?)×H0k(?)中存在唯一的整体解;然后,采用紧致法证明了该问题生成的解半群S(t)存在一个紧的整体吸引子族Ak;最后,通过线性化方法,证明了算子半群S(t)的Frechet可微性以及关于线性化问题体积元的衰减性,从而得到整体吸引子族的Hausdorff维数和Fractal维数估计.
The initial-boundary value problems for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations is studied.Firstly,the existence and uniqueness of the global solution of the equation in space H0m+k(?)×H0k(?)prove that the solution semigroup S(t)generated by the problem has a compact global attractor family Ak.Finally,the semigroup of operators is proved by linearization method.The Hausdorff dimension and Fractal dimension estimation of the global attractor family are obtained by using the Frechet differentiability and the attenuation of the volume element for the linearization problem.
作者
林国广
朱昌清
LIN Guo-guang;ZHU Chang-qing(School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2019年第5期867-875,共9页
Journal of Yunnan University(Natural Sciences Edition)
基金
国家自然科学基金(11561076)
