一类拟线性抛物型偏微分方程在非光滑复连通区域初边值问题的广义解存在唯一性

THE EXISTENCE AND UNIQUENESS OF THE INITIAL-BOUNDARY VALUE PROBLEM OF A QUASILINEAR PARABOLIC EQUATION IN NON-SMOOTH DOUBLY CONECTED REGION

本文讨论了一类拟线性复连通域上抛物方程非光滑边界的边值问题,给出了广义解的存在唯一性定理。

Describ the temperature fild of large concrete dam value prnblem of above eqatuion in non-somooth douly by quasilinear parabolic equation: u_t=1/(c(x,u)ρ(x,u))[K_(ij)(x,u,u_x)_u_x_j]=(F(x,t,u))/(c(x,u)ρ(x,u)). We obtain the existence and uniqueness of the initial-boundary conected region: =u(x,t,u) =f1(t),u(x,0)=u_0(x), determin the state space of this systerm,and make a basis for getting its optimal boundary control.