一类非线性反应扩散方程爆破时间的下界估计

Lower Bound Estimates of Blow-up Time for a Class of Nonlinear Reaction-diffusion Equations

研究了三维有界区域上非线性反应扩散方程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.在某种特殊的限定条件下,证明了全局解的存在性.

The finite time blow-up problem of the solution of nonlinear reaction-diffusion equation in three dimensional bounded domain is studied.Assuming that the solution satisfies the nonlinear conditions at the boundary of the region,the lower bound of the blow-up time are obtained by constructing the auxiliary function and using the energy estimation method and the differential inequality technique when the blow-up occurs.The existence of global solutions is proved under some special limiting conditions.