Blow-up problem for a nonlinear diffusion equation and its diffusion coefficient

本研究计画致力于研究非线性热方程爆破问题与扩散系数之间的关系。特别地，我研究了小扩散情形下爆破集位置的刻画，在本计划的第一年，我应用小扩散爆破问题的结果，证明了环上非线性热方程在边界上爆破的径向对称解的不存在性，在本计划的最后一年，研究了一类具有一般非线性项（包括指数非线性项）的超线性热方程的爆破问题。特别是，我的特点是位置的爆破组的解决方案，小扩散。

This research program is devoted to the study of the relationship between the blow-up problem for a nonlinear heat equation and the diffusion coefficient. In particular, I have studied the characterization of the location of the blow-up set under a small diffusion situation.In the first year of this program, I applied the results of the blow-up problem with small diffusion, and proved the non-existence of the radially symmetric solution which blows up on the boundary for a nonlinear heat equation on an annulus.In the final year of this program, I have studied the blow-up problem for a superlinear heat equation with general nonlinearity including exponential nonlinearity. In particular, I characterized the location of the blow-up set of solutions with small diffusion.