Volume 18, Issue 1, March 2011, Pages 139 - 149
Global Existence and Blow-Up Phenomena for the Periodic Hunter–Saxton Equation with Weak Dissipation
Authors
Xuemei Wei
Faculty of Applied Mathematics, Guangdong University of Technology, 510006 Guangzhou, P. R. China,wxm_gdut@163.com
Zhaoyang Yin
Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, P. R. China,mcsyzy@mail.sysu.edu.cn
Received 17 May 2010, Accepted 25 September 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001246How to use a DOI?
- Keywords
- The Hunter–Saxton equation; weak dissipation; blow-up; blow-up rate; global solution
- Abstract
In this paper, we study the periodic Hunter–Saxton equation with weak dissipation. We first establish the local existence of strong solutions, blow-up scenario and blow-up criteria of the equation. Then, we investigate the blow-up rate for the blowing-up solutions to the equation. Finally, we prove that the equation has global solutions.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Xuemei Wei AU - Zhaoyang Yin PY - 2021 DA - 2021/01/07 TI - Global Existence and Blow-Up Phenomena for the Periodic Hunter–Saxton Equation with Weak Dissipation JO - Journal of Nonlinear Mathematical Physics SP - 139 EP - 149 VL - 18 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001246 DO - 10.1142/S1402925111001246 ID - Wei2021 ER -