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| Content Provider | Springer Nature Link |
|---|---|
| Author | Liu, Zhengrong Tang, Hao Shi, Shijie |
| Copyright Year | 2014 |
| Abstract | This paper is concerned with the periodic boundary problem for the b-family equation. At first, we use a different method to prove the local well-posedness in the critical Besov space $$B_{2,1}^{3/2}$$ . Then we show that if a weaker $$B_{p,r}^q$$ -topology is used, the solution map becomes Hölder continuous. Moreover, we show that the dependence on initial data is optimal in $$B_{2,1}^{3/2}$$ in the sense that the solution map is continuous but not uniformly continuous. Finally, we obtain the periodic peaked solutions to the b-family equation and apply them to obtain the ill-posedness in $$B_{2,\infty }^{3/2}$$ . |
| Ending Page | 492 |
| Page Count | 22 |
| Starting Page | 471 |
| File Format | |
| ISSN | 00269255 |
| e-ISSN | 14365081 |
| Journal | Monatshefte für Mathematik |
| Issue Number | 3 |
| Volume Number | 177 |
| Language | English |
| Publisher | Springer Vienna |
| Publisher Date | 2014-08-14 |
| Publisher Place | Vienna |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Periodic peaked solutions Ill-posedeness Dependence of solutions on initial and boundary data, parameters Existence problems: global existence, local existence, non-existence KdV-like equations (Korteweg-de Vries) Initial-boundary value problems for nonlinear higher-order equations Periodic boundary value problem Mathematics b-family equation Well-posedness |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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