As was shown by Kaper and Kwong Diierential and Integral Equations 3, 353{362], there exists a unique R > 0, such that the diierential equation u 00 + 2 + 1 r u 0 + u ? u q = 0; r > 0; (0 q < 1, 0) admits a classical solution u, which is positive and monotone on (0; R) and which satisses the boundary conditions u 0 (0) = 0; u(R) = u 0 (R) = 0: In this article it is shown that u(0) is bounded, b...

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...