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Blowing-up solutions of the time-fractional dispersive equations

Authors
  • Alsaedi, Ahmed1
  • Ahmad, Bashir1
  • Kirane, Mokhtar1, 2
  • Torebek, Berikbol T.3, 4, 5
  • 1 King Abdulaziz University, P.O. Box 80203, 21589 , (Saudi Arabia)
  • 2 Khalifa University of Science and Technology, United Arab Emirates , (United Arab Emirates)
  • 3 Al–Farabi Kazakh National University, Al–Farabi ave. 71, 050040 , (Kazakhstan)
  • 4 Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., 050010 , (Kazakhstan)
  • 5 Logic and Discrete Mathematics Ghent University, Krijgslaan 281 , (Belgium)
Type
Published Article
Journal
Advances in Nonlinear Analysis
Publisher
De Gruyter
Publication Date
Jan 12, 2021
Volume
10
Issue
1
Pages
952–971
Identifiers
DOI: 10.1515/anona-2020-0153
Source
De Gruyter
Keywords
License
Green

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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