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.
Highlights
Nonlinear wave phenomenon is one of the important areas of scienti c investigation
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 modi ed Korteweg-de Vries-Burgers equations on a bounded domain
Among the mathematical models describing the dynamics of wave equations include Korteweg-de Vries equation, Burgers equation, Benjamin-Bona-Mahony equation, Rosenau equation and Ostrovsky equation
Summary
Nonlinear wave phenomenon is one of the important areas of scienti c investigation. Among the mathematical models describing the dynamics of wave equations include Korteweg-de Vries equation, Burgers equation, Benjamin-Bona-Mahony equation, Rosenau equation and Ostrovsky equation.Bateman-Burgers equation or Burgers equation [6, 9]ut + uux = νuxx, ν > , (1.1)is a fundamental partial di erential equation occurring in various areas of applied mathematics, such as uid mechanics, nonlinear acoustics, gas dynamics, tra c ow.The Korteweg-de Vries equation [16] is well known in di erent elds of science and technology, it reads ut + uux + uxxx = . (1.2)This work is licensed under the Creative Commons AttributionA. In [19,20,21,22,23] Korpusov et al obtained su cient conditions for the nite time blow-up of solutions of initialboundary problems for Burgers, Korteweg-de Vries, Benjamin-Bona-Mahony and Rosenau type equations. Blowing-up solutions of the time-fractional Rosenau-KdV-BBM-Burgers equation with initial conditions described as follows:
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