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.

中文翻译：

---

时间分数阶色散方程的爆破解

摘要 本文致力于研究 Korteweg-de Vries、Benjamin-Bona-Mahony、Burgers、Rosenau、Camassa-Holm、Degasperis-Procesi、Ostrovsky 和时间分数修正 Korteweg 的时间分数类似物的初边界值问题。 -de Vries-Burgers 方程在有界域上。给出了上述方程在有限时间内爆破的充分条件。我们还讨论了梯度非线性对时间分数 Burgers 方程初边值问题全局可解性的最大原理和影响。我们研究的主要工具是 Pohozhaev 非线性容量方法。我们还提供了一些说明性示例。