Partial symmetry of initial value problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:450

Article

Zhang, Zhi-Yong¹ 

[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

关键词: Partial symmetry;    Exact symmetry;    Initial value problems;    Invariant solution;   

DOI  :  10.1016/j.jmaa.2017.01.054

来源: Elsevier

【 摘 要 】

It is generally believed that the symmetry of initial value problems (IVP) must leave both the partial differential equations (PDEs) and initial conditions invariant. In this paper, we propose partial symmetry of IVP which needs less restrictive conditions on the PDEs and initial conditions and only leaves the IVP invariant on some non-empty subset of the whole solution set of the governing PDEs. Thus some symmetries which either only leave the PDEs invariant or only leave initial conditions invariant are partial symmetries of IVP. Then considering from two different starting points, we define two types of partial symmetry and give the corresponding algorithms where one starts with the PDEs and the other is from the initial conditions. Applications to Boussinesq equation and a class of nonlinear heat equation are performed. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free