Solving the dam problem by means of optimal control over domain (Q1909822)

We present a method to solve a dam problem, which is based on its reduction to a problem on optimal control over a domain. Into the coast functional we include the \(L_2\)-norm of normal component of the filtration velocity on the free boundary, which enables us to construct a finite-dimensional approximation. We prove solvability of the problem of optimal control and of the problem with penalty, as well as convergence of solutions with penalty to the solution of original problem.