How would the "a" and "c" coefficients be defined in a coupled non-linear set of 2 PDEs?

I have these two coupled non-linear set of PDEs that I have expressed in the standard MATLAB PDE form:

Would pdesolve be able to take c_1 and c_2 as functions of the state variable u_2; and a_2 as a function of the state variable u_1? If so, would "c" and "a" be 2 x 2 matrices?

Answer 1

[Alan Weiss]

Assuming that you can represent your geometry and boundary conditions properly, then the answer is yes, you can formulate your coefficients for nonlinear problems like this. See the documentation on specifying coefficients, and in particular the section on the c coefficient.

Alan Weiss

MATLAB mathematical toolbox documentation

[Shashank]

Thank you Alan. I am carefully reading the documentation on c and a coefficients.

With respect to boundary conditions, does this toolbox allow periodic boundary conditions? I only see Dirichlet, Neumann and mixed conditions on the documentation.

[Alan Weiss]

Sorry, no, there are no periodic boundary conditions allowed.

Alan Weiss

MATLAB mathematical toolbox documentation