Symmetry analysis, conserved quantities and applications to a dissipative DGH equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Wei, Long¹  Wang, Yang¹ 

[1] Hangzhou Dianzi Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

关键词: Lie symmetry analysis;    Conserved quantity;    Blow-up analysis;    Wave-breaking;    Weak peakon-type solution;   

DOI  :  10.1016/j.jde.2018.08.055

来源: Elsevier

【 摘 要 】

In this paper, we study a weakly dissipative Dullin-Gottwald-Holm equation from the viewpoint of Lie symmetry analysis. We first perform symmetry analysis and the nonlinear self-adjointness of this equation. Due to a mixed derivatives term in the equation, we need to rewrite the corresponding form Lagrangian in symmetric form to construct conservation laws. From the viewpoint, we present a general procedure of how these conserved quantities come about. Based on these conserved quantities, blow-up analysis and global existence of strong solutions are presented. Finally, we show that this equation admits a weak peakon-type solution. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free