Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case

Fast Numerical Methods for Bernoulli Free Boundary Problems

The numerical solution of the free boundary Bernoulli problem is addressed. An iterative method based on a level-set formulation and boundary element method is proposed. Issues related to the implementation, the accuracy and the generality of the method are discussed. The efficiency of the approach is illustrated by numerical results.

Robust Duality for Generalized Convex Programming Problems under Data Uncertainty∗

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model...

Boundary Control of a Bernoulli Free Boundary Problem

We present a boundary optimal control approach for a Bernoulli free boundary problem. Our control objective consists in tracking a free boundary to an a priori given desired one. An appropriate cost functional is chosen for this purpose and its gradient is analytically derived. The resulting optimality conditions are discretized and the minimization problem is solved numerically by a steepest d...

A Parabolic Free Boundary Problem with Bernoulli Type Condition on the Free Boundary

Consider the parabolic free boundary problem ∆u− ∂tu = 0 in {u > 0} , |∇u| = 1 on ∂{u > 0} . For a realistic class of solutions, containing for example all limits of the singular perturbation problem ∆uε − ∂tuε = βε(uε) as ε → 0, we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary ∂{u > 0} can be decomposed into an ...

On Free Boundary Problems