摘要
本文用概率方法讨论了如下拟线性扩散方程的广义Dirichlet问题。1/2△u(x)+q(x)u(x)+f(x,u)=(u(x)/t)x=(x,t)∈Dlim u(x)=(z),z∈D∩(D^c)~r且z为连续点 (D→x→z)其中D为d+1维欧氏空间R^d中的一个有界区域, D表D的边界,q∈K_d,q在D Holder连续,f(x,y)(x∈D,y∈R′)是满足一定光滑性的非线性函数, 是 D上本质有界,本质连续函数。给出了使上述问题有界解存在唯一的定理。
This paper is aimed tto give a probabilistic treatment of the generalized Dirichlet problem for the qusi-Linear equation on DWhere D be a bounded domain in tthe d+1 - dimensional Euclidean space Rd, D is the boundary of D,q∈ka and q is Holder continuous on D, f(x,y)(x∈D,y∈R1) is a nonlinear sufficient smooth functcon, be essentially bounded and essentially continuous on D. The existence and uniqueness theorms for bounded solution are given.
