Volume 15, Issue Supplement 2, August 2008, Pages 28 - 49
Blow-Up Phenomena and Decay for the Periodic Degasperis-Procesi Equation with Weak Dissipation
Authors
Shuyin Wu, Zhaoyang Yin
Corresponding Author
Shuyin Wu
Received 5 February 2008, Revised 25 April 2008, Available Online 1 August 2008.
- DOI
- 10.2991/jnmp.2008.15.s2.3How to use a DOI?
- Abstract
In the paper, several problems on the periodic Degasperis-Procesi equation with weak dissipation are investigated. At first, the local well-posedness of the equation is established by Kato’s theorem and a precise blow-up scenario of the solutions is given. Then, several critera guaranteeing the blow-up of the solutions are presented. Moreover, the blow-up rate and blow-up set of the blowing-up solutions are discussed. Furthermore, it is proved that the equation has global solutions and these global solutions decay to zero as time goes to infinite provided the potentials associated to their initial date are of one sign.
- Copyright
- © 2008, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Shuyin Wu AU - Zhaoyang Yin PY - 2008 DA - 2008/08/01 TI - Blow-Up Phenomena and Decay for the Periodic Degasperis-Procesi Equation with Weak Dissipation JO - Journal of Nonlinear Mathematical Physics SP - 28 EP - 49 VL - 15 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2008.15.s2.3 DO - 10.2991/jnmp.2008.15.s2.3 ID - Wu2008 ER -