一类具有混合扩散的抛物型方程解的正则性

The regularity of solutions for a class of parabolic equation with mixed diffusion operators

对于R^(N)(N≥2)上一类具有局部和非局部混合扩散算子的非线性抛物型方程,利用反证法,通过构造爆破序列,并结合经典的刘维尔型定理,给出了其弱解的正则性估计证明.

In this paper, the author considers the nonlinear parabolic equation with mixed local and nonlocal diffusion operators on R^(N). Using inverse proof method, the regularity estimation of weak solutions is proved by constructing the blow-up sequence and combining with the classical Liouville-type theorem.