On the Inverse Problem for the Ekman Equation

Abstract

We consider inverse problems for the partial differential equation Δu - 2h -1 (⊇h, ⊇u) = g. We assume that the unknown function u - the stream function for a class of flow problems - is constant on certain parts of the boundary ∂Ω while at the remaining parts no boundary condition is imposed. Instead, values of the gradient of u (velocities) are prescribed at a finite set M of inner points (measuring points). We look for the minimizer of a functional being a combination of the squared errors at the measuring points and - for regularization - a squared H 1/2 -norm ofthe (unknown) boundary values. We present numerical solutions to the problem. Especially, the dependence on the regularization parameter μ is discussed.