A free boundary problem in accretive growth

We study a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation within a prescribed constraining set. Existence, variational representability, and regularity of solutions to the growth subproblem are investigated. The full system arises from coupling the growth dynamics with an elliptic equation for the activation field. Existence of solutions to the fully coupled free boundary problems is obtained via an iterative procedure.