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I am trying to solve a PDE, but Mathematica is showing a strange message which is saying" boundary condition is not specified on a single edge"


a = 0.1;
b = 0.55;
U11[t_, r_] = D[U1[t, r], r];
U22[t_, r_] = D[U2[t, r], r];
V11[t_, r_] = D[V1[t, r], r];
V22[t_, r_] = D[V2[t, r], r];
sol2 = Flatten[
  NDSolve[{D[U1[t, r], 
      t] == (D[U1[t, r], {r, 2}] + 1/r D[U1[t, r], {r, 1}]) - 
      U1[t, r] - U1[t, r] + V1[t, r] + 
      2, (D[V1[t, r], {r, 2}] + 
        1/r D[V1[t, r], {r, 1}]) + ((U1[t, r])^2/
        2 + (D[U1[t, r], {r, 1}])^2) + ((U1[t, r])^2 + 2) == 
     D[V1[t, r], t], 
    D[ U2[t, r], t] == 
     2 + (D[U2[t, r], {r, 2}] + 1/r D[U2[t, r], {r, 1}]) - U2[t, r] - 
      U2[t, r] + V2[t, r] + 
      2, (D[V2[t, r], {r, 2}] + 
        1/r D[V2[t, r], {r, 1}]) + ((U2[t, r])^2/
        2 + (D[U2[t, r], {r, 1}])^2) + (U2[t, r])^2 + 2 == 
     D[V2[t, r], t], U1[0, a] == 0, U2[0, b] == 0, V1[0, a] == 0, 
    V2[0, b] == 0, U1[t, a] == 0, V1[t, a] == 0, U2[t, 1] == 0, 
    V2[t, 1] == 1, U1[t, b] == U2[t, b], V1[t, b] == V2[t, b], 
    U11[t, b] == U22[t, b], V11[t, b] == V22[t, b]}, {U1, U2, V1, V2},
    t, r], 1]

Mathematically the condition is sufficient for those Pde, but still, Mathematics is showing an error, is there any modification can i make in the code? Thanks with regards.

Improve this question
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  • $\begingroup$ NDSolve[…, t, r] is obviously wrong. Notice NDSolve is a numeric solver and you need to specify the range of t and r. Please read the document of NDSolve for more info. $\endgroup$
    – xzczd
    Jan 27 at 3:17

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