LONGTIME BEHAVIOR FOR THE ACTIVATOR-INHIBITOR MODEL

作     者：WU Jianhua(Department of Mathematics, Shaanxi Normal University, Xi’an 710062, China)HUANG Aixiang(Department of Mathimatics, Xi’an Jiaotong University, Xi’an 710049, China) 

作者机构：陕西师范大学数学系 陕西 西安 710062 西安交通大学数学系 陕西 西安 

出 版 物：《Systems Science and Mathematical Sciences》 (SYSTEMS SCIENCE AND MATHEMATICAL SCIENCES)

年 卷 期：2000年第13卷第3期

页      面：285-291页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：国家自然科学基金 

主　　题：Maximal attractor estimate of dimension inertial manifold activatorinhibitor model 

摘      要：The paper first discusses the longtime behavior of the activator-inhibitor model, the existence of the maximal attractor is given. Then using the mathematical induction and the properties of linear semigroup, the regularity result for the maximal attractor is obtained. Next, it is proved that its Hausdorff or fractal dimension is ***, further estimates are verilied by Rothe’s inequality and fractional operators, and the existence of inertial manifold is then proved.