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Homework Help: Derive the minimization problem corresponding to a given PDE, with boundary condition

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Let Ω[itex]\subset[/itex]R2 be a region with boundary [itex]\Gamma[/itex]=[itex]\Gamma[/itex]1[itex]\bigcup[/itex][itex]\Gamma[/itex]2. On Ω we must solve the PDE

    [tex]-{div}(\frac{h^{3}}{12\mu}{grad} p+\frac{h}{2}{u})+kp=f[/tex]

    with h and f functions of the spatial coordinates, \mu and k given constants, u a given constant velocity vector and the pressure p unknown. The boundary conditions fot this PDE are:

    p = p0 on [itex]\Gamma[/itex]1

    (n, \frac{h^{3}}{12\mu}{grad} p+\frac{h}{2}{u} ) = 0 on [itex]\Gamma[/itex]2

    n is the outward normal and p0 a given pressure.

    Derive the minimization problem corresponding to the PDE, with boundary conditions.

    Can anyone give me some hints about this problem? I don't know where to start.
    Thanks in advance! :)
  2. jcsd
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