广义双色散热耦合方程组的初边值问题  

Initial boundary value problems for the generalized double dispersion thermoelastic coupled equations

作　　者：李娜 张建文 LI Na;ZHANG Jianwen(Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《纯粹数学与应用数学》2023年第1期52-71,共20页Pure and Applied Mathematics

基　　金：国家自然科学基金(11872264).

摘　　要：研究了一类广义双色散热耦合方程组的初边值问题在齐次边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性;其次通过证明系统的衰减性和渐近紧性,得到了系统存在全局吸引子;最后证明了该系统的全局吸引子存在有限分形维数.The attractors of the initial boundary value problem for a class of the generalized double dispersion thermoelastic coupled equations under homogeneous boundary conditions are studied.First,the existence and uniqueness of global solutions is proved by Faedo-Galerkin method.Second,by proving the declinability and asymptotic compactness of the system,the existence of global attractors is obtained.Finally,it is proved that the global attractor of the system has finite fractal dimension.

关 键 词：热耦合 整体解 全局吸引子 有限分形维数 

分 类 号：O175.2[理学—数学]