Geodesic
Blow-up of solutions to a periodic nonlinear dispersive rod equation
Documenta mathematica, Tome 15 (2010), pp. 267-283

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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.
DOI : 10.4171/dm/298
Classification : 30C70, 37L05, 58E35
Mots-clés : singularity, best constant, convolution problem, rod equation 
Liangbing Jin; Yongming Liu; Yong Zhou. Blow-up of solutions to a periodic nonlinear dispersive rod equation. Documenta mathematica, Tome 15 (2010), pp. 267-283. doi: 10.4171/dm/298
@article{10_4171_dm_298,
     author = {Liangbing Jin and Yongming Liu and Yong Zhou},
     title = {Blow-up of solutions to a periodic nonlinear dispersive rod equation},
     journal = {Documenta mathematica},
     pages = {267--283},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/298},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/298/}
}
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