Coupled partial differential equations

I have 5 coupled partial differential equations in t and r ( second order). Is therre someone who can help me to implement these equations in FreeFem? I am new in FreeFem and used Mathematica.

We need the equations more less to help you,
and to know if is possible solve it with freefem++

Dear Frederic,

Thanks for your reaction. I attached the equations

I also attached the mathematica file.

Hope you have suggestions.

Best regards

Reinoud

(Attachment PDEs slagter.docx is missing)

(Attachment spinn CS Mondi Marder t-dep-A.nb is missing)

Dear Frederic,

Thanks for your reply.

I send you my equations and also the Mathematica file. Hopr you can help

Best regards

Reinoud

slagter.zip (1.15 MB)

Real, I do not, your equation are complex ,and fully no linear,

You can try but it is not easy.

I think your equation come format quantum mechanics.

If you need help, do you have a papier to explain how this equations are build, because
it is a really no standard equation. for a mathematician.

you can send directly the mail to frederic.hecht@sorbonne-universite.fr

best regard.

Dear Frederic,

Thanks for your reply. Indeed, these equations originate from my research on cosmic strings. The 3 PDE’s for the metric ( in general relativity, mu,xi and J) are the problem. They are extracted from the Einstein equations, but the system is overdetermined,
so I can write the 3 PDE’s in different form, i.e., for example such that they become parabolic. For example with diff(J,t,t) = diff(J,r,r) …

The 5 PDE’s I send you is one possible isolation of the equations for mu, xi and J.

The 2 PDE’s forthe matter field, X and P are fixed.

I send you the maple 18 file, where you can read off the Einstein equations for mu,xi and J

(Attachment Slagter-2.docx is missing)

Dear Frederic,

Thanks for your reply. Indeed, these equations originate from my research on cosmic strings. The 3 PDE’s for the metric ( in general relativity, mu,xi and J) are the problem. They are extracted from the Einstein equations, but the system is overdetermined,
so I can write the 3 PDE’s in different form, i.e., for example such that they become parabolic. For example with diff(J,t,t) = diff(J,r,r) …

The 5 PDE’s I send you is one possible isolation of the equations for mu, xi and J.

The 2 PDE’s for the matter field, X and P are fixed.

I send you the maple 18 file, where you can read off the Einstein equations for mu,xi and J

Best regards

Reinoud

slagter2.zip (2.1 MB)

Dear Reinoud;

I have no real idea to solve numerical you pdf.

Bien cordialement,
Frédéric Hecht.