一类非线性抛物型方程的最优系统和对称破缺  

Optimal systems and symmetry breaking for a class of nonlinear parabolic equations

作　　者：付丽敏 王丽真 闫璐 Fu Limin;Wang Lizhen;Yan Lu(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China;Department of Mathematics,Northwest University,Xi'an 710127,China;Faculty of Science,Xijing University,Xi'an 710123,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211 [2]西北大学数学学院,陕西西安710127 [3]西京学院理学院,陕西西安710123

出　　处：《纯粹数学与应用数学》2021年第4期450-465,共16页Pure and Applied Mathematics

基　　金：国家自然科学基金(11971251)。

摘　　要：研究了一类非线性抛物型方程的对称群、最优系统和对称破缺.首先给出了这个方程的七维的李对称群,利用伴随作用的不变量,建立了其李对称群的最优系统.在此基础上,构建了二维和三维最优系统,并研究了该方程的对称破缺,基于其最优系统的子代数,给出了更一般的一类抛物型方程的分类.In this paper, symmetry groups, optimal systems and symmetry breaking of a class of nonlinear parabolic equations are studied. Firstly, the seven-dimensional Lie symmetry group of the equation is given, and the one-dimensional optimal systems of the Lie symmetry group by invariants of the adjoint representation is constructed. Based on one-dimensional optimal systems, the two-dimensional and three-dimensional optimal systems of the symmetry group are derived. Finally, symmetry breaking of the equation is also studied. In terms of the subalgebra of the optimal systems, a classification to the more general class of parabolic equations is provided.

关 键 词：非线性抛物型方程 对称群 微分不变量 最优系统 对称破缺 

分 类 号：O175.27[理学—数学]