The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation
A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign conditi...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/532369 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value
u0 satisfies the sign condition and u0∈Hs(R) (s>3/2), it is shown that there exists a unique
global solution for the equation in space C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)). |
|---|---|
| ISSN: | 1085-3375 1687-0409 |