How solve two partial differential equations on two coupled regions with a shared boundary condition?

Hi,

The mathematical model consists of two PDEs, one for each rectangular region, but they share a Neumann-type boundary condition at the union of both rectangles, the description of the model is as follows:

Region 1, rectangular: ,

PDE 1

Region 2, rectangular: ,

PDE 1

The shared boundary condition between both Partial Differential Equations is at , such a boundary condition is:

at

I have been trying to bind this boundary condition using MATLAB Toolbox "pdetool", but I have not succeeded.

Thank you for your time.

[Torsten]

First of all, correct the mathematics of your problem: You need two interface conditions at y = R1, not only one.