I just see this pde: $$u_t=\epsilon^2u_{xx}-u,\ \ 0<\epsilon<<1 \\ \text{with conditions:}\ \ \ \ \ \ \ u(x,0)=1-x,\ u(0,t)=1,\ u(1,t)=0$$
and would like to know how it can be derived from a specific heat transfer problem. I plot this pde numerically in Matlab and it shows me the formation of a boundary layer near $x=0$
as time increases from 0. So can anyone help me an application of heat transfer leads to having this form of a pde? Would really appreciate it.