带耗散项的p-方程组的周期BV解  

Periodic BV Solution of p-Equations with Dissipative Terms

作　　者：丁倩茹 DING Qian-ru(School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《西安文理学院学报（自然科学版）》2020年第4期1-5,11,共6页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(10571120)。

摘　　要：主要研究有部分耗散项的p方程组的周期解并说明当时间趋于无穷时解的指数衰减性.首先对p方程组做出基本假设,主要是满足弱耗散性假设及kawashima条件,接下来利用能量方法来证明带耗散项p方程组解的衰减性,最后结合随机取点法在小初值的情况下可以构建方程的局部解,并由原系统所对应的矩阵满足对角占优的性质,进而得出原系统的BV解的指数衰减性.In this paper,the periodic solutions of p-equations with partial dissipative term were mainly studied,and the exponential decay of solutions when time tends to infinity was illustrated.Firstly,some basic assumptions about the p-equations were made,which mainly satisfy the weak dissipation assumption and kawashima condition.Then,the energy method was used to prove the decay of the solutions of p-equations with dissipative term.Finally,the local solution of the equation can be constructed with the method of random sampling,and the exponential decay of BV solution of the original system is obtained by the diagonal dominance of the matrix corresponding to the original system.

关 键 词：耗散项 对角占优 能量方法 周期解 局部解 随机取点 BV解 小初值 

分 类 号：O193[理学—数学]