Hello,
I'm trying to solve the system like this. The main problem is piecewise initial conditions. I tried to use Piecewise function in Mathematica, but Mathematica throws an error
"The first argument {1,0<=thet<=\[Pi]/6} of Piecewise is not a list \
of pairs. "
What is my mistake? Here's the code
c = 100;
b = 1;
a = 1.01;
mu = 1;
r0 = 0.1;
w = NDSolve[{D[u[r, thet, t], t] ==
D[u[r, thet, t], {r, 2}] + (1/r) D[u[r, thet, t], r] + (1/r^2) D[
u[r, thet, t], {thet, 2}] +
u[r, thet, t] (1 - u[r, thet, t] - c*x[r, thet, t]),
D[x[r, thet, t], t] ==
mu*(D[x[r, thet, t], {r, 2}] + (1/r) D[x[r, thet, t],
r] + (1/r^2) D[x[r, thet, t], {thet, 2}]) +
a*x[r, thet, t] (1 - c*u[r, thet, t] - b*x[r, thet, t]),
D[u[r, thet, t], r] == 0 /. {r -> 1},
D[x[r, thet, t], r] == 0 /. {r -> 1},
u[r, thet, 0] ==
Piecewise[{{Piecewise[{1, 0 <= thet <= Pi/6}, {0,
Pi/6 < thet < 2 Pi}], r <= r0}}, {0, r > r0}],
x[r, thet, 0] == u[r, thet, 0] ==
Piecewise[{{Piecewise[{0, 0 <= thet <= Pi/6}, {1,
Pi/6 < thet < 2 Pi}], r <= r0}}, {0, r > r0}],
}, {u[r, thet, t], x[r, thet, t]}, {t, 0, 100}, {r, 0, 1}, {thet,
0, 2 Pi}]
Thanks!
