Hello, please I 'm really stuck in this program, I can't find the error, I really need to solve this problem If anyone can help me, please
T = 2 \[Pi];
l = \[Pi];
a = 1/2;
w1 = 2 \[Pi];
(*Définit la fonction indicatrice*)
indicator[x_] := Piecewise[{{1, 0 < x < \[Pi]/2}}, 0];
S[x_, t_] := Sum[ Exp[- t n^2] Integrate[x Sin[s n^2], {s, 0, \[Pi]}] Sin[x n^2], {n, 5}]
(*controllability map*)
G[x_, t_] := indicator[x] S[x, T - t]
(*Grammian operator Q*)
Q[x_, t_] := (indicator[x])^2 Integrate[(S[x, T - s])^2, {s, T - l, T}]
(*inverse function*)
v[x_, t_] := InverseFunction[a + Q][x, t];
(*Test*)
v[w1 - S[1, T],T]