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Blow-up of solutions to a nonlinear dispersive rod equation

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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.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200062, China

    Yong Zhou

  2. The Institute of Mathematical Sciences, The Chinese University of Hong Kong Shatin, N.T., Hong Kong

    Yong Zhou

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  1. Yong Zhou
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Correspondence to Yong Zhou.

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

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Zhou, Y. Blow-up of solutions to a nonlinear dispersive rod equation. Calc. Var. 25, 63–77 (2006). https://doi.org/10.1007/s00526-005-0358-1

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  • DOI: https://doi.org/10.1007/s00526-005-0358-1

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