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March 16, 2010 9:37am UTC

help on a hard question:1d but two variables

Hello, everyone:

I am studying an electromagnetic model:

-d/dz(D(z)d/dz)C(z,q) + D(z)*q^2*C(z,q) =1
where
1/D(z)=integral(dq*q*C).

z is a space variable, and q is not a space variable(frequency value). So it is a 1D question in fact but there are two variables in the equation.

Is it possible to design two sub-domains, one for z and the other for q?

Thanks a lot!

Hao

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March 17, 2010 12:57pm UTC in response to hao zhang

Re: help on a hard question:1d but two variables

Dont know about the convergence or even the existence of solution but if I had to solve something like that, I will use a 2d pde on a rectangle domain , the variable being z the other q.
calculate D as a projection coupling variable on the z axis and write your first equation as a pde on the rectangle . Of course the boundary conditions will need to be properly written.
Good luck
jf

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