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help on a hard question:1d but two variables

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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

2 Replies Last Post 17.03.2010, 08:57 GMT-4

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Posted: 1 decade ago 17.03.2010, 08:48 GMT-4
Is there anyone who is willing to help me solve this problem? Or just give me some hints on how to solve it. Thanks!
Is there anyone who is willing to help me solve this problem? Or just give me some hints on how to solve it. Thanks!

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Posted: 1 decade ago 17.03.2010, 08:57 GMT-4
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
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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