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

1. Nov 29, 2011

### yakamozyu

1. The problem statement, all variables and given/known data

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

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

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 $\Gamma$1

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

n is the outward normal and p0 a given pressure.

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