Parabolic Problems

Abstract

The form of the time-dependent PDE system solved by PDE/PROTRAN (Section 1.5) is:

$$\begin{array}{*{20}{c}} {C(x,y,t,u){u_t}) = {A_x}(x,y,u,{u_x},{u_y}) + {B_y}(x,y,t,u,{u_x},{u_y}) + F(x,y,t,u,{u_x},{u_y})\,in\,R} \\ {u = FB(x,y,t)\,on\,\partial {R_1}} \\ {A{n_x} + B{n_y} = GB(x,y,t,u)\,on\,\partial {R_2}} \\ {u = UO(x,y)\,at\,t = {t_0}} \end{array}$$

((4.1.1))

where R is a general two dimesional region, $\partial {R_1}\,and\,\partial {R_2}$ are disjoint parts of the boundary, and C is a diagonal m by m matrix (m=number of PDEs).