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I want to solve a 2D-PDE that has the form

NDSolve[{D[u[t, x], t] == 
    D[(u[t, x]*(u[t, x]^2 - u0^2) - D[u[t, x], x, x]), x, x],
   u[0, x] == 0,
   u[t, 0] == 0,
   u[t, 5] == 0}, u, {t, 0, 10}, {x, 0, 5}];

However, I would like to have periodic boundary conditions, how do I specify these?

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  • $\begingroup$ As much as I know only linear PDE solvers are implemented. For nonlinear ones we still wait. $\endgroup$
    – Alexei Boulbitch
    Mar 13 '15 at 13:04
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NDSolve[{D[u[t, x], t] == 
   D[(u[t, x]*(u[t, x]^2 - u0^2) - D[u[t, x], x, x]), x, x], u[0, x] == 0, 
  u[t, 0] == u[t, 5]}, u, {t, 0, 10}, {x, 0, 5}]

You'd need to specify u0 which was not given in the question.

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