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Let Ω[itex]\subset[/itex]R^{2}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]

withhandffunctions of the spatial coordinates, \mu andkgiven constants,ua given constant velocity vector and the pressurepunknown. The boundary conditions fot this PDE are:

p=p_{0}on [itex]\Gamma[/itex]_{1}

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

nis the outward normal andp_{0}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! :)

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

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