Blowing-up solutions of the time-fractional dispersive equations
Alsaedi A. Ahmad B. Kirane M. Torebek B.T.
1 January 2021De Gruyter Open Ltd
Advances in Nonlinear Analysis
2021#10Issue 1952 - 971 pp.
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.
Benjamin-Bona-Mahony equation , blow-up , Burgers equation , Camassa-Holm equation , Caputo derivative , Korteweg-de Vries equation , Ostrovsky equation , Rosenau equation
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NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
Department of Mathematics and Statistics, College of Art and Sciences, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
Al-Farabi Kazakh National University, Al-Farabi ave. 71, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics Ghent University, Krijgslaan 281, Ghent, Belgium
NAAM Research Group
Department of Mathematics and Statistics
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
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