一类广义Boussinesq方程局部弱解的存在唯一性  

Existence and Uniqueness of Local Weak Solution for a Class of Generalized Boussinesq Equations

作　　者：唐自敏 秦敏 原子霞[1] TANG Zimin;QIN Min;YUAN Zixia(School of Mathematical Sciencs,University of Electronie Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《四川轻化工大学学报（自然科学版）》2020年第3期68-74,共7页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：教育部人文社会科学研究青年基金项目(15YJC790132)。

摘　　要：在三维空间的情形下,对一类非线性广义Boussinesq方程的Cauchy问题进行研究,利用Galerkin方法证明问题的局部弱解是存在且唯一的。首先选取适当的逼近解,借助Sobolev空间中的一些基本不等式,建立关于逼近解的能量估计式,利用能量估计式和弱收敛定理,证明问题存在一个局部弱解。最后利用证明能量估计式的过程中得到的结论对局部弱解的唯一性进行证明。In the case of three-dimensional space,the Cauchy problem of a class of nonlinear generalized Boussinesq equation is studied. The Galerkin method is used to prove that the local weak solution of the problem exists and is unique.Firstly,the appropriate approximation solution is selected,and then an energy estimation formula for the approximation solution is established by using some basic inequalities in Sobolev space. By using the energy estimation formula and weak convergence theorem,it is proved that the problem has a local weak solution. Finally,the uniqueness of the local weak solution is proved by the conclusion obtained in the process of proving the energy estimation.

关 键 词：广义BOUSSINESQ方程 GALERKIN方法 存在性 唯一性 

分 类 号：O175.29[理学—数学]