一类二阶拟线性偏微分方程粘性解的存在性

Existence of Viscosity Solutions of a Class of Quasilinear Degenerate Parabolic Equations

讨论如下Dirichlet问题:ut-Tr[a(t,x)D2u]+H(t,x,u,Du)=0(t,x)∈QT=(0,T)×Ωu(t,x)=ψ(t,x)(t,x)∈PQT证明了该问题的比较原理,进而获得粘性解的存在性。

The following Dirichlet problem is considered {ut-Tr[a（t,x）D^2u]＋H（t,x,M,Du）=0 （t,x）∈QT=（0,T）×Ω u（t,x）=ψ（t,x） （t,x）∈δPQT The comparison theorem is proved, moreover, using the comparison theorem, the existence of viscosity solutions is obtained.