I have the following system of PDEs:
Where: phi(d,e,f,g,h,j,k)
and c1-c8 are real valued constants
I coded it into mathematica like this:
eqns = {C1*k*D[phi[d, e, f, g, h, j, k], g] -
C2*f*D[phi[d, e, f, g, h, j, k], k] +
C1*k*D[phi[d, e, f, g, h, j, k], f] -
C3*k*D[phi[d, e, f, g, h, j, k], d] == 0,
C1*k*D[phi[d, e, f, g, h, j, k], h] -
C2*g*D[phi[d, e, f, g, h, j, k], k] +
C4*k*D[phi[d, e, f, g, h, j, k], j] -
C3*k*D[phi[d, e, f, g, h, j, k], e] == 0,
C5*k*D[phi[d, e, f, g, h, j, k], d] -
C2*h*D[phi[d, e, f, g, h, j, k], k] -
C6*k*D[phi[d, e, f, g, h, j, k], g] -
C6*k*D[phi[d, e, f, g, h, j, k], f] == 0,
C5*k*D[phi[d, e, f, g, h, j, k], e] -
C2*j*D[phi[d, e, f, g, h, j, k], k] -
C7*k*D[phi[d, e, f, g, h, j, k], j] +
C8*k*D[phi[d, e, f, g, h, j, k], j] -
C6*k*D[phi[d, e, f, g, h, j, k], h] == 0}
And called Dsolve:
Dsolve[eqns, phi[d, e, f, g, h, j, k], phi[d, e, f, g, h, j, k]]
Unfortunately Dsolve is not able to solve it.
I formulated these PDEs from an engineering problem and to the best of my knowledge it should have atleast 4 solutions to it.
I want to know if this is beyond mathematica's ability to solve or if I did some preprocesssing of some kind if it would help?
I am just starting to learn about PDEs so I'm not quite sure what I could do from my end to help Mathematica solve it.
DSolve
rather thanDsolve
. Even with the correct spelling, it does not return a result. Are you sure that analytical solutions exist? Could you say more about where the equations come from? $\endgroup$ – MarcoB Jun 21 '18 at 2:14