Calculus of Variations and Partial Differential Equations

, Volume 25, Issue 1, pp 63–77

Blow-up of solutions to a nonlinear dispersive rod equation

Original Article

DOI: 10.1007/s00526-005-0358-1

Cite this article as:
Zhou, Y. Calc. Var. (2006) 25: 63. doi:10.1007/s00526-005-0358-1

Abstract

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.

Keywords

Best constantConvolution problemRod equationSingularity

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina
  2. 2.The Institute of Mathematical SciencesThe Chinese University of Hong Kong ShatinN.T.