一类带位势非线性热方程解的不存在性定理

A nonexistence theorem to the nonlinear heat equations with potentials

研究与向量场有关的非线性次椭圆热方程.通过选取合适的测试函数,应用反证法证明了与之相关的初边值问题解的不存在性定理,将欧式空间及Heisenberg群上的结果推广至满足Hrmander有限秩条件的光滑向量场.

In this paper we consider the nonlinear subelliptic heat equations related to a system of vector fields. By choosing proper test functions and using contradiction arguments, a nonexistence theorem to the corresponding initial-boundary value problem is proved, thus the known results in Euclidean space are extended to the smooth vector fields satisfying HSrmander＇s finite rank condition.