ABSTRACT

This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, by combining Hardy inequality, ‘moving’ potential well methods with some differential inequalities. Moreover, the upper and lower bounds for the blow-up time are also derived when blow-up occurs.

中文翻译：

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具有特殊扩散过程的反应扩散方程的爆破现象

摘要

本文关注具有特殊扩散过程的反应扩散方程的初始边值问题解的爆破性质。结果表明，在初始数据的某些条件下，通过将 Hardy 不等式、“移动”势井方法与一些微分不等式相结合，该问题的解决方案在有限时间内爆炸。此外，当发生爆破时，还导出了爆破时间的上限和下限。