摘要
本文研究非线性波动与神经传播混合型方程u_tt＝u_xxt＋σ（u_x）_x－h（u）u_t-f（u）＋g（x）初边值问题的整体吸引子.在σ∈C^2,σ＇（s）＞σo＞0及h（s）∈C^1,－Co＜）且∫~u_oh（s）sds＞0）条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性，并证明了它具有有限的Hausdorff维数和fractal维数．
This paper deals with the universal attractor of initial-boundary value problemfor mixed equations of nonlinear wave and nerve conduct u_tt=u_xxt+σ(u_x)_x-h(u)u_t-f(u)+g(x).Under the assumptions σ∈C^2,σ'(s)>σo>oh(s)∈C^1, -Co<h(s) (o<Co< ) and ∫~u)o h(s)s ds<Cu^2 (C>o),we obtain the existence of universal compact attractor of this problem. Its Hausdorff andfractal dimensions are proved to be finite.
出处
《应用数学学报》
CSCD
北大核心
1998年第3期339-352,共14页
Acta Mathematicae Applicatae Sinica
关键词
非线性波方程
神经传播方程
整体吸引子
Nonlinear wave equation, nerve conduct equation, universal attractor,dimension
