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arXiv · 1901.09246

Blowing-up solutions of the time-fractional dispersive equations

Bashir Ahmad·Ahmed Alsaedi·Mokhtar Kirane·Berikbol T. Torebek
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Abstract

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

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Bashir Ahmad, Ahmed Alsaedi, Mokhtar Kirane, Berikbol T. Torebek. 2020-02-20. Blowing-up solutions of the time-fractional dispersive equations. https://doi.org/10.1515/anona-2020-0153

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