Journal of Nonlinear Mathematical Physics

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
Available Online 1 August 2008.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - 100
Pages
28 - 49
Publication Date
2008/08
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2008.15.s2.3How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Shuyin Wu
AU  - Zhaoyang Yin
PY  - 2008
DA  - 2008/08
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  - https://doi.org/10.2991/jnmp.2008.15.s2.3
ID  - Wu2008
ER  -