Blow-up of solutions to a nonlinear dispersive rod equation |
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| Authors: | Yong Zhou |
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| Affiliation: | (1) Department of Mathematics, East China Normal University, Shanghai, 200062, China;(2) The Institute of Mathematical Sciences, The Chinese University of Hong Kong Shatin, N.T., Hong Kong |
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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. Mathematics Subject Classification (2000) 30C70, 37L05, 35Q58, 58E35 |
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| Keywords: | Best constant Convolution problem Rod equation Singularity |
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