Blow-up of solutions to a periodic nonlinear dispersive rod equation
Summary: In this paper, first 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 to blow up in finite time. We also analyze the corresponding ordinary difference equation associated to the convolution problem and give a numerical simulation for the optimal constant.
scientific article; zbMATH DE number 5706086