I have a system of coupled PDEs relatd to the heat equation that I am trying to solve using the 'pdepe' command in Matlab. The equations are as follows-
Here, 'T' and 'm' are the independent variables and 't' is time. A(m, T) is a function of both 'm' and 'T' while k(T) is a function of T only. B is a constant. The initial conditions are as follows-
(T0 is a constant)
The boundary conditions are-
I know how to use pdepe when only one independent variable is there but with two I am having trouble casting these equations in the matrix form that is expected by the solver. Any help is appreciated!