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Thread Subject:
Challenge: system of nonlinPDE equations

Subject: Challenge: system of nonlinPDE equations

From: Baha Kuzu

Date: 4 Jul, 2013 05:36:10

Message: 1 of 1

Hi all,
I have a PDE problem with 4 variables. Equations are in the parabolic form. There are coupling in boundary conditions. I don't know if it can be solved with pde-toolbox. Any comments/suggestions for solving the problem is appreciated.

Problems with u1, u2, u3, u4 variables and c1,c2,...c7 constants;
Geometry of a Rectangle with width=2d and height=h; t: time;
x-y coordinate is placed in the middle of base edge (width);

You can check the problem I explained from this link: https://plus.google.com/photos/112656951672093634355/albums/5896627951601137601?authkey=COyr_8f8m5uh1wE

Or I described it as following:

** Eq-1
D(u1)/Dt - c1*D^2(u1)/Dx^2-c1*D^2(u1)/Dy^2=0
** BCs & IC
@x=0 -> D(u1)/Dx = 0;
@x=d -> D(u1)/Dx = 1/c1*(c2*u4 - c3*u1*(c4 - u4));
@y=0 -> D(u1)/Dy =-1/c1*(c2*u4 - c3*u1*(c4 - u4));
@y=h -> u1 =c5*exp(-t);
@t=0 -> u1 =c5;
%%%%%%%%%%%%%%%%%
** Eq-2
D(u2)/Dt - c1*D^2(u2)/Dx^2-c1*D^2(u2)/Dy^2=0
** BCs & IC
@x=0 -> D(u2)/Dx = 0;
@x=d -> D(u2)/Dx = 0;
@y=0 -> D(u2)/Dy = 0;
@y=h -> u2 = 1/2*[sqrt(c5^2*exp(-2t) + 4*c6) - c5*exp(-t)];
@t=0 -> u2 = 1/2*[sqrt(c5^2 + 4*c6) - c5];
%%%%%%%%%%%%%%%%%
** Eq-3
D(u3)/Dt - c1*D^2(u3)/Dx^2-c1*D^2(u3)/Dy^2=0
** BCs & IC
@x=0 -> D(u3)/Dx = 0;
@x=d -> D(u3)/Dx = 0;
@y=0 -> D(u3)/Dy = 0;
@y=h -> u3 = 1/2*[sqrt(c5^2*exp(-2t) + 4*c6) + c5*exp(-t)];
@t=0 -> u2 = 1/2*[sqrt(c5^2 + 4*c6) + c5];
%%%%%%%%%%%%%%%%%
** Eq-4
D(u4)/Dt - c3*u1*(c4 - u4) + c2*u2=0
** IC
@t=0 -> u4 = 0;
%%%%%%%%%%%%%%%%%

Do you know if the pde-toolbox can handle this problem? Any comments/suggestions for solving the problem is appreciated. Thanks in advance...

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