Hi,
There are two issues you have to consider in constructing your model:
- Defining the geometry that includes the subdomain boundaries.
- Defining the coefficients that presumably vary from subdomain to subdomain.
The second issue can be dealt with in the pdetool GUI by entering the coefficient as a string expression that includes the variables x and y or by entering the name of a MATLAB function where the coefficients are calculated. However, I don't know how to define the geometry using mathematical expressions in the GUI. So I recommend you create your entire model and calculate the solution by calling the PDE Toolbox functions from a MATLAB script. All of the examples shown on the following documentation page take this approach:
Documentation for defining your own geometry can be found here: http://www.mathworks.com/help/pde/ug/pdegeom.html
Documentation for writing a function to define your coefficients can be found here: http://www.mathworks.com/help/pde/ug/scalar-coefficients-in-function-form.html
The following example shows a case where the coefficients vary by subdomain (but are linear): http://www.mathworks.com/help/pde/examples/deflection-of-a-piezoelectric-actuator.html
Extending this example to a case where the coefficients are also functions of the solution, u, should be straightforward.
Bill
