Paper Info
Title
On the optimal control for a semilinear equation with cost depending on the free boundary.
Abstract
We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The new aspect considered in this paper, with respect to other control problems involving free boundaries, is that here the cost functional explicitly depends on the location of the free boundary. The main difficulty is to show the continuous dependence (in measure) of the free boundary with respect to the control function. The crucial tool to get such continuous dependence is to know how behaves the state solution near the free boundary, as in previous works by L.A. Caffarelli and D. Phillips among other authors. Here we improved previous results in the literature thanks to a suitable application of the Fleming-Rishel formula.
Year
DOI
Venue
2012
10.3934/nhm.2012.7.605
NETWORKS AND HETEROGENEOUS MEDIA
Keywords
Field
DocType
Optimal control,semilinear equations,free boundary
Boundary value problem,Robin boundary condition,Mathematical optimization,Boundary (topology),Mathematical analysis,Free boundary problem,Singular boundary method,Neumann boundary condition,Mathematics,Elliptic boundary value problem,Mixed boundary condition
Journal
Volume
Issue
ISSN
7
SP4
1556-1801
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
J. I. Díaz162.53
Tommaso Mingazzini200.34
A.M. Ramos3175.46