Blow-up of solutions to the DGH equation |
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Authors: | Yong Zhou |
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Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, China |
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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. |
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Keywords: | Best constant Convolution problem Integrable equation Singularity |
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