Blowing-up solutions of the time-fractional dispersive equations

Advances in Nonlinear Analysis

Torebek Berikbol T.¹  Ahmad Bashir²  Kirane Mokhtar²  Alsaedi Ahmed² 

[1] Al–Farabi Kazakh National University, Al–Farabi ave. 71, 050040, Almaty, Kazakhstan;NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia;

关键词: caputo derivative;    burgers equation;    korteweg-de vries equation;    benjamin-bona-mahony equation;    camassa-holm equation;    rosenau equation;    ostrovsky equation;    blow-up;    primary 35b50;    secondary 26a33;    35k55;    35j60;   

DOI  :  10.1515/anona-2020-0153

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown