# Help!! I can't find the error in this program? (InverseFunction)

Posted 2 years ago
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 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] 
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Posted 2 years ago
 What is indicator[x]?
Posted 2 years ago
 Sorry, I forget to add indicator[x]. I edit the question: (*Définit la fonction indicatrice*) indicator[x_] := Piecewise[{{1, 0 < x < \[Pi]/2}}, 0]; do you have any idea why it doesn't work ? this is error i get : NDSolve::underdet: There are more dependent variables, {f[x,t],InverseFunction[1/2+Q][x,t]}, than equations, so the system is underdetermined. 
Posted 2 years ago
 Hmmmm, what do you understand by InverseFunction[a + Q] ????I assume that this is nonsense.Look at ContourPlot[a + Q[x, y], {x, .5, 1}, {y, 4, 5}] and you see that there are really many combinations of x and y giving the same value of a + Q [x, y], so the inverse function is not really existing.For example a + Q[.5397, 4.651] a + Q[.87921, 4.243] So what do expect as result of InverseFunction[ a + Q ] ?
Posted 2 years ago
 Hi Hans, As you said InverseFunction[ a + Q ] for me is the inverse of 1/2+Q. But it doesn't have any sense I think the problem is in S[x,t], I just test It's not working !! can you see it, please!Best regards,
Posted 2 years ago
 InverseFunction[ a + Q ] for me is the inverse of 1/2+Q. OK, but this does (in general) not exist. So - what do you expect of a non-existing function in your equations?S looks indeed somewhat peculiar, but I can't see why there should be a problem. S[x_, t_] := Sum[-Exp[-t n^2] (\[Pi] Cos[\[Pi] n^2])/(n^2) Sin[x n^2], {n, 5}] Plot3D[S[x, t], {x, 0, \[Pi]}, {t, 0, T}, PlotRange -> All, PlotPoints -> 50] `Why don't you tell us about the physical problem you want to describe. I got the feeling that your equations are somewhat strange.
Posted 2 years ago
 Hi Mr. Hans, I just edit my question, I've just noticed that there are some mistakes in my original question, I've changed it completely. but I still have in the inverse !!
Posted 2 years ago
 OK. But as this inverse does not exist there seems to be something severely wrong with your model.
Posted 2 years ago
 Duplicate of this question.