一类无穷阶退化抛物方程解的存在性

Existence of Solutions for a Class of Infinitely Degenerate Parabolic Equations

设X=（X1…，Xm）是一组无穷阶退化向量场，△x=∑mj=1Xj＊Xj，其中Xj＊j是Xj形式自伴算子．运用不动点理论得到抛物方程ut=△xu＋ulog｜u｜解的存在性．

Let X = （X1,..., Xm） be an infinitely degenerate system of vector fields, m , △x=∑mj=1Xj＊Xj, where Xj＊ is the formal adjoint of Xj. By employing the fixed point theorem, we obtain the existence of solutions to the degenerate parabolic equation ut =△xu＋ulog｜u｜.