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On the optimal control for a semilinear equation with cost depending on the free boundary

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Díaz Díaz, Jesús Ildefonso and Mingazzini, Tomasso and Ramos del Olmo, Ángel Manuel (2012) On the optimal control for a semilinear equation with cost depending on the free boundary. Networks and Heterogeneous Media, 7 (4). pp. 605-615. ISSN 1556-1801

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Official URL: https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8051


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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.


Item Type:Article
Uncontrolled Keywords:Optimal control; semilinear equations; ofree boundary.
Subjects:Sciences > Mathematics > Operations research
ID Code:29436
Deposited On:13 Apr 2015 10:37
Last Modified:12 Dec 2018 15:07

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