Blowing-up solutions of the time-fractional Burgers, Korteweg-de Vries, Benjamin-Bona-Mahony, Rosenau and Ostrovsky type equations
Ahmad, Bashir ; Alsaedi, Ahmed ; Kirane, Mokhtar ; Torebek, Berikbol T.
arXiv, Tome 2019 (2019) no. 0, / Harvested from
This paper is devoted to the initial-boundary value problem for the time-fractional analogues of Korteweg-de Vries-Benjamin-Bona-Mahony-Burgers, Rosenau-Kortweg-de Vries-Benjamin-Bona-Mahony-Burgers, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions of the blow-up of global solutions in finite time of above equations are considered. We also study the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. In closing, we provide the some exact examples. The proof of the results is based on the Mitidieri-Pohozhaev nonlinear capacity method.
Publié le : 2019-01-26
Classification:  Mathematics - Analysis of PDEs 
@article{1901.09246,
     author = {Ahmad, Bashir and Alsaedi, Ahmed and Kirane, Mokhtar and Torebek, Berikbol T.},
     title = {Blowing-up solutions of the time-fractional Burgers, Korteweg-de Vries,
  Benjamin-Bona-Mahony, Rosenau and Ostrovsky type equations},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.09246}
}

Ahmad, Bashir; Alsaedi, Ahmed; Kirane, Mokhtar; Torebek, Berikbol T. Blowing-up solutions of the time-fractional Burgers, Korteweg-de Vries,
  Benjamin-Bona-Mahony, Rosenau and Ostrovsky type equations. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.09246/