Blowing-up solutions of the time-fractional dispersive equations

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.

Keywords

• caputo derivative
• burgers equation
• korteweg-de vries equation
• benjamin-bona-mahony equation
• camassa-holm equation
• rosenau equation
• ostrovsky equation
• blow-up
• primary 35b50
• secondary 26a33
• 35k55
• 35j60