Blowing-up solutions of the time-fractional dispersive equations-Reference-Cited by-同舟云学术

Blowing-up solutions of the time-fractional dispersive equations

Published:2021-01-01 Issue:1 Volume:10 Page:952-971
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Alsaedi Ahmed¹,Ahmad Bashir¹,Kirane Mokhtar¹²,Torebek Berikbol T.³⁴⁵

Affiliation:

1. NAAM Research Group, Department of Mathematics, Faculty of Science , King Abdulaziz University , P.O. Box 80203 , Jeddah , 21589 , Saudi Arabia

2. Department of Mathematics and Statistics, College of Art and Sciences , Khalifa University of Science and Technology , Abu Dhabi , United Arab Emirates

3. Al–Farabi Kazakh National University , Al–Farabi ave. 71, 050040 , Almaty , Kazakhstan

4. Institute of Mathematics and Mathematical Modeling , 125 Pushkin str., 050010 , Almaty , Kazakhstan

5. Department of Mathematics: Analysis , Logic and Discrete Mathematics Ghent University , Krijgslaan 281 , Ghent , Belgium

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0153/pdf

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