Date: 25 Oct 2005

Blow-up of solutions to a nonlinear dispersive rod equation

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In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions.

Mathematics Subject Classification (2000) 30C70, 37L05, 35Q58, 58E35