带梯度吸收项的快扩散方程的自相似奇性解

Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms

研究一类带有非线性梯度吸收项的快速扩散方程的自相似奇性解.通过自相似变换,该自相似奇性解满足一个非线性常微分方程的边值问题,再利用打靶法技巧研究该常微分方程初值问题解的存在唯一性并根据初值的取值范围对其解进行了分类.通过对这些解类的性质的分析研究,得出了自相似强奇性解存在唯一性的充分必要条件,此时自相似奇性解就是强奇性解.

The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms had been studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ODE. Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE had been investigated, the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and solutions. In case of existence, the self-similar singular solution is very singular solution.