Blow-up of Solutions to a Periodic Nonlinear Dispersive Rod Equation

In this paper, firstly we find an optimal constant for a convolution problem on the unit circle via the variational method. Then by using the optimal constant, we give a new and improved sufficient condition on the initial data to guarantee the corresponding strong solution blows up in finite time. We also analyze the corresponding ordinary difference equation associate to the convolution problem and give numerical simulation for the optimal constant.

2010 Mathematics Subject Classification: Primary 30C70; Secondary 37L05, 35Q58, 58E35.

Keywords and Phrases: best constant, convolution problem, rod equation, singularity.

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