## Reaction Diffusion System,

I have a problem solving a numerical reaction diffusion equation. It leads to the following answer:

`RecursionLimit::reclim2: "Recursion depth of 1024 exceeded during evaluation`

How can I solve this problem? My PC is quite fast, and I am willing to run it over night if necessary. But first of course I want to check if my equations are all right. How can I figure out working parameters and boundary conditions?

Thanks for help.

Here is the code (Derived from an old Maple code of mine and a code I found here in the *Mathematica* Stack Exchange):

```
ClearAll;
(*Parameter*)
da = 1;
db = 0.1;
k = 10;
(*Gleichungssytem und NDSolve*)
a1 = {D[a1[t, x, y], t] ==
da*D[a1[t, x, y], x, x] + da*D[a1[t, x, y], y, y] - k*a1[t, x, y]};
a2 = {D[a2[t, x, y], t] ==
db*D[a2[t, x, y], x, x] + db*D[a2[t, x, y], y, y] - k*a2[t, x, y]};
a3 = {D[a3[t, x, y], t] ==
da*D[a3[t, x, y], x, x] + da*D[a3[t, x, y], y, y] +
k*a3[t, x, y](*-D[a4[t,x,y]]*)};
Ω =
ImplicitRegion[0 <= x <= 100 && 0 <= y <= 100, {x, y}];
(*Lösung des Gleichungssystems*)
soln = NDSolve[{a1, a2, a3, (*a4*)},
Derivative[0, 1, 0][a1][t, 0, y] == 0,
Derivative[0, 1, 0][a1][t, 100, y] == 0,
Derivative[0, 0, 1][a1][t, x, 0] == 0,
Derivative[0, 0, 1][a1][t, x, 100] == 0,
a1[0, x, y] == 100, a1, {x, 0, 100}, {y, 0, 100}, {t, 0, 10},
Derivative[0, 1, 0][a2][t, 0, y] == 0,
Derivative[0, 1, 0][a2][t, 100, y] == 0,
Derivative[0, 0, 1][a2][t, x, 0] == 0,
Derivative[0, 0, 1][a2][t, x, 100] == 0,
a2[0, x, y] == 0, a2, {x, 0, 100}, {y, 0, 100}, {t, 0, 10},
Derivative[0, 1, 0][a3][t, 0, y] == 0,
Derivative[0, 1, 0][a3][t, 100, y] == 0,
Derivative[0, 0, 1][a3][t, x, 0] == 0,
Derivative[0, 0, 1][a3][t, x, 100] == 0,
a3[0, x, y] == 0, a3, {x, 0, 100}, {y, 0, 100}, {t, 0, 10},
(*Plotausgabe a1*)
Plot3D[a1[t, x, 1] /. soln, {t, 0, 10}, {x, 0, 100},
PlotStyle -> Gray]
(*Plotausgabe a2*)
Plot3D[a2[t, x, 1] /. soln, {t, 0, 10}, {x, 0, 100},
PlotStyle -> Pink]
(*Plotausgabe a3*)
Plot3D[a3[t, x, 1] /. soln, {t, 0, 10}, {x, 0, 100},
PlotStyle -> Green]
```