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Hiroki
11/29/08 02:47am

Please help someone.
Nice to meet you.
I want to analayz "nonlinear reaction-diffusion equation".
But, I couldn't fit the "Boundary and Initial condition".
Please help and ,teach that source code.


pde = {D[a[t, x, y], t] ==
Subscript[D, a] {D[a[t, x, y], x, x] + D[a[t, x, y], y, y]} +
Subscript[\[Rho], a]
a[t, x, y]^2/({1 + Subscript[k, a] a[t, x, y]^2} h[t, x, y]) -
Subscript[\[Mu], a] a[t, x, y] + Subscript[\[Sigma], a],
D[h[t, x, y], t] ==
Subscript[D, h] {D[h[t, x, y], x, x] + D[h[t, x, y], y, y]} +
Subscript[\[Rho], h] a[t, x, y]^2 -
Subscript[\[Mu], h] h[t, x, y] + Subscript[\[Sigma], h]};

bc = {(D[a[t, x, y], x] /. x -> -4) ==
0, (D[a[t, x, y], x] /. x -> 4) ==
0, (D[a[t, x, y], y] /. y -> -4) ==
0, (D[a[t, x, y], y] /. y -> 4) ==
0, (D[h[t, x, y], x] /. x -> -4) ==
0, (D[h[t, x, y], x] /. x -> 4) ==
0, (D[h[t, x, y], y] /. y -> -4) ==
0, (D[h[t, x, y], y] /. y -> 4) == 0,
a[0, x, y] == Exp[-(x^2 + y^2)], h[0, x, y] == Exp[-(x^2 + y^2)]};

sol = First[
NDSolve[{pde, bc}, {a[t, x, y], h[t, x, y]}, {t, 0, 2}, {x, -4,
4}, {y, -4, 4}]]

Thanks

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Subject (listing for 'simultaneous partial differential equation')
Author Date Posted
simultaneous partial differential equation Hiroki 11/29/08 02:47am
Re: simultaneous partial differential equation niels 12/03/08 10:24am
Re: Re: simultaneous partial differential equat... Hiroki 12/07/08 12:42pm
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