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This could be a stupid issue, but I have been checking for ages. I cannot solve this apparently innocuous system of PDEs:

L = 10; \[Xi] = 1; DD = 1; Subscript[\[Phi], 0] = 1;
l = 1; w = 0.13;
 v = 0.1; \[Eta] = 0.5; DD = 1; \[Lambda] = 0.1;

\[CapitalOmega] = l \[Pi]/ L ; 

Equations 


u[\[Alpha]aa_, a_, A_] = -(1/(2 \[Eta] + \[Lambda]^2*(a +A E^(-Subscript[\[Phi], 
       0] - \[Phi][x] Cos[\[CapitalOmega] x]))*
  Sin[2 \[Theta][x] Sin[\[CapitalOmega] x]]^2))*((a + 
    A E ^(Subscript[\[Phi], 
      0] + \[Phi][x] Cos[\[CapitalOmega] x])) \[Lambda] w (D[\[Theta][
      x] Sin[\[CapitalOmega] x], x])^2 \[CapitalOmega]^2 Sin[
   2  \[Theta][x] Sin[\[CapitalOmega] x]] Sin[\[Theta][
     x] Sin[\[CapitalOmega] x]]^2 - 
 2*(a +A E^(-Subscript[\[Phi], 0] - \[Phi][x] Cos[\[CapitalOmega] x]))*
  v*(Subscript[\[Phi], 0] + \[Phi][x] Cos[\[CapitalOmega] x])^2 \[Theta][
   x]  \[CapitalOmega] Cos[\[CapitalOmega] x]  Sin[\[Theta][
     x] Sin[\[CapitalOmega] x]] + (a +A E^(-Subscript[\[Phi], 
       0] - \[Phi][
        x] Cos[\[CapitalOmega] x]))*\[Alpha]aa*(Subscript[\[Phi], 
    0] + \[Phi][x] Cos[\[CapitalOmega] x])^2*
  Sin[2 \[Theta][x] Sin[\[CapitalOmega] x]] + 
 D[\[Phi][x] Sin[\[CapitalOmega] x], 
   x] \[CapitalOmega]  Cos[\[Theta][
     x] Sin[\[CapitalOmega] x]] (w - \[Lambda] w Cos[
      2 \[Theta][x] Sin[\[CapitalOmega] x]]));


eqn1[\[Alpha]aa_, a_, A_] := (-D[\[Theta][x]*Sin[\[CapitalOmega] x], {x, 2}]*(1 - 
   w Cos[\[Theta][x]*Sin[\[CapitalOmega] x]]^2) (a + 
   A E^(Subscript[\[Phi], 0] + \[Phi][x] Cos[\[CapitalOmega] x])) + 
1/2 (a + A E^(
    Subscript[\[Phi], 
     0] + \[Phi][
       x] Cos[\[CapitalOmega] x])) w^2 \[CapitalOmega]^2 (D[\[Theta][
     x] Sin[\[CapitalOmega] x], x])^2 Sin[
  2 \[Theta][x] Sin[\[CapitalOmega] x]] - (Subscript[\[Phi], 
   0] + \[Phi][x] Cos[\[CapitalOmega] x]) (a + 
   A  E^(-Subscript[\[Phi], 
      0] - \[Phi][x] Cos[\[CapitalOmega] x]))  v   D[\[Theta][
    x] Sin[\[CapitalOmega] x], 
  x] \[CapitalOmega]  Sin[\[Theta][x]*Sin[\[CapitalOmega] x]] - 
u[\[Alpha]aa, a, 
  A] (1 - \[Lambda] Cos[2 \[Theta][x] Sin[\[CapitalOmega] x]]) - (a + 
   A E^(Subscript[\[Phi], 
     0] + \[Phi][x] Cos[\[CapitalOmega] x])) w  \[CapitalOmega]  D[\[Phi][
    x]  Sin[\[CapitalOmega] x], 
  x] Cos[\[Theta][x]*Sin[\[CapitalOmega] x]]);


eqn2[\[Alpha]aa_, a_, A_] := -D[( 
 v (a + A E^(-Subscript[\[Phi], 
        0] - \[Phi][x] Cos[\[CapitalOmega] x])) (Subscript[\[Phi], 
     0] + \[Phi][x] Cos[\[CapitalOmega] x])^2 Sin[\[Theta][
      x] Sin[\[CapitalOmega] x]] - (DD (1 - \[Xi] Sin[\[Theta][
            x] Sin[\[CapitalOmega] x]]^2) - 
     w Cos[\[Theta][x] Sin[\[CapitalOmega] x]]^2) (a + 
     A E^(Subscript[\[Phi], 
       0] + \[Phi][x] Cos[\[CapitalOmega] x])) \[CapitalOmega] D[\[Phi][
      x] Cos[\[CapitalOmega] x], x] + \[Lambda]  u[\[Alpha]aa, a, 
    A] Sin[\[Theta][x] Sin[\[CapitalOmega] x]] Sin[
    2 \[Theta][x] Sin[\[CapitalOmega] x]]), x]; 

Solving

 sol1 = {\[Theta], \[Phi]} /. First[NDSolve[{
  eqn1[0.07, 0, 1] == 0,
  eqn2[0.07, 1, 0] == 0, 
  \[Theta][0] == 0,
  \[Theta][L] == 0,

\!\(\*SuperscriptBox["\[Phi]", 
TagBox[
RowBox[{"(", "1", ")"}],
Derivative],
MultilineFunction->None]\)[0] == 0,

\!\(\*SuperscriptBox["\[Phi]", 
TagBox[
RowBox[{"(", "1", ")"}],
Derivative],
MultilineFunction->None]\)[L] == 0}, {\[Theta], \[Phi]}, {x, 0, L}] ];

\[Infinity]::indet: Indeterminate expression 0. ComplexInfinity encountered. >>

\[Infinity]::indet: Indeterminate expression 0. ComplexInfinity encountered. >>

\[Infinity]::indet: Indeterminate expression 0. ComplexInfinity encountered. >>

General::stop: Further output of \[Infinity]::indet will be suppressed during this calculation. >>

NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.`. >>

ReplaceAll::reps: {<<1>>==0,<<10>>+(0.1 <<2>> (<<1>>))/(1.+<<21>> <<1>>)==0,\[Theta][0]==0,\[Theta][10]==0,(\[Phi]^\[Prime])[0]==0,(\[Phi]^\[Prime])[10]==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
share|improve this question
    
First of all, try not to use capital (DD), and subscripted symbols. Also, please remove non-code lines (like Equations) and the actual output from your code, and present output as separate block (using Ctrl+Q). Also, u should be defined with := instead of =. –  István Zachar Dec 13 '13 at 8:37

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