Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592365 | Journal of Functional Analysis | 2007 | 22 Pages |
Abstract
In this paper, firstly we find best constants for two convolution problems on the unit circle via a variational method. Then we apply the best constants on a nonlinear integrable shallow water equation (the DGH equation) to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Finally, we discuss the blow-up phenomena for the nonperiodic case.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory