一个微分不等式及在CH方程中的应用

A First Order Differential Inequality and Its Application to CH Equation

研究一个一阶微分不等式,探究满足该不等式的函数所具有的性质,并将其应用到CamassaHolm方程的研究中,给出了Camassa-Holm方程解的爆破条件、解的爆破速率和爆破时间的估计.

Differential inequalities are widely applied in the study of differential equations. In this paper, we study a new differential inequality and apply it to the classical Camassa-Holm （CH） equation. We obtain the existence of blow-up solution of the CH equation, and the estimates of blow- up time and blow-up rate are derived.