Blowing-up solutions of the time-fractional dispersive equations
Ahmed AlsaediNAAM Research Group, Department of Mathematics, Faculty of Science , King Abdulaziz University , P.O. Box 80203 , Jeddah , 21589 , Saudi ArabiaBashir AhmadNAAM Research Group, Department of Mathematics, Faculty of Science , King Abdulaziz University , P.O. Box 80203 , Jeddah , 21589 , Saudi ArabiaMokhtar KiraneDepartment of Mathematics and Statistics, College of Art and Sciences , Khalifa University of Science and Technology , Abu Dhabi , United Arab EmiratesBerikbol T. TorebekAl–Farabi Kazakh National University , Al–Farabi ave. 71, 050040 , Almaty , Kazakhstan
2021en
ABI
Аннотация
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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