# Question:How do I solve a system of PDE's in terms of other functions?

## Question:How do I solve a system of PDE's in terms of other functions?

Maple

I have a system of PDE's - 14 equations.  I am trying to solve for 9 functions in terms of other functions.  I thought I was doing this correctly.  I have:

> sys := [EQNSub[0], EQNSub[1], EQNSub[2], EQNSub[3], EQNSub[4], EQNSub[5], EQNSub[6], EQNSub[7], EQNSub[8], EQNSub[9], EQNSub[10], EQNSub[11], EQNSub[12], EQNSub[13]];

sysl := subs(l[0] = -1, sys);

pdsolve(sysl, [a[0], a[1], a[2], b[0], b[1], b[2], c[0], c[1], c[2]]);
----------------------OUTPUT---------------------------

The second line is just me defining a parameter in the system.  Everything checks out until the last step.  In other words, I know the system is correct.  The a,b and c's are functions of x,y and t.  I want to solve the system for them.  In the equations, EQNSub[i],  functions p and q, where p = p(x,t) and q = q(y,t), and their derivatives appear.  I want to solve the system basically considering p,q and their derivatives as constants.

A typical EQNSub[i] is:
0 = a[0, t] + a[0, x, x, x] + 3 a[1] q[y] c[0] + 3 b[1] p[x] a[0]

+ 3 a[1] p[x] b[0] + 3 c[1] q[y] a[0] + 6 a[2] p[x] p[x, x]

+ 6 a[2] q[y] q[y, y] + a[0, y, y, y] - 3 a[1, y] q[y, y] - a[1] q[y, y, y]

- 3 a[1, y, y] q[y] - 3 a[1, x, x] p[x] - 3 a[1, x] p[x, x]

2              3
- a[1] p[x, x, x] - a[1] p[t] - a[1] q[t] + 6 a[2, y] q[y]  + 2 a[1] p[x]

3                 2
+ 2 a[1] q[y]  + 6 a[2, x] p[x]  - 3 b[0, x] a[0] - 3 a[0, x] b[0]

- 3 c[0, y] a[0] - 3 a[0, y] c[0],

I thought this last line would do that.  When I attempt to solve the system it just gets stuck computing.  Is it possible it could take 20min+?  I have an older chip - Pentium 4, but still....

Any suggestions?

Thanks,
Ryan

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