二维有界区域上具有非线性梯度项的抛物系统解的存在性

Existence of Solutions for Parabolic Systems with Nonlinear Gradient Terms in Two Dimensional Bounded Regions

研究了二维有界区域上带非线性梯度项的一类抛物方程的解在有限时间的爆破问题.假设解在区域的边界上满足非线性条件,当爆破发生时,通过构造辅助函数,利用能量估计的方法和微分不等式技术,得到了爆破时间的下界.对方程中的参数做出一定的限制之后,证明了全局解的存在性.

In this paper,the blow-up problem in finite time for solution of a class of parabolic equations with nonlinear gradient term in two-dimensional bounded domain was studied.Assuming that the solutions satisfied the nonlinear conditions on the boundary of the region,the lower bound of the blow-up time could be obtained by constructing the auxiliary function,using the energy estimation method and the differential inequality technique when the blow-up occurred.After limiting the parameters in the equation,the existence of global solutions were proved.