Geodesic
On the maximization problem for solutions of reaction–diffusion equations with respect to their initial data
Grégoire Nadin1 ; Ana Isis Toledo Marrero2
1 Sorbonne Université, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France.
2 Université Paris Nord, Institut Galilée, UMR 7539, LAGA, 93430 Villetaneuse, France.
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 71.

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We consider in this paper the maximization problem for the quantity ∫ Ωu(t, x)dx with respect to u0 =: u(0, ⋅), where u is the solution of a given reaction diffusion equation. This problem is motivated by biological conservation questions. We show the existence of a maximizer and derive optimality conditions through an adjoint problem. We have to face regularity issues since non-smooth initial data could give a better result than smooth ones. We then derive an algorithm enabling to approximate the maximizer and discuss some open problems.
DOI : 10.1051/mmnp/2020030

Grégoire Nadin 1 ; Ana Isis Toledo Marrero 2

1 Sorbonne Université, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France.
2 Université Paris Nord, Institut Galilée, UMR 7539, LAGA, 93430 Villetaneuse, France. 
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Grégoire Nadin; Ana Isis Toledo Marrero. On the maximization problem for solutions of reaction–diffusion equations with respect to their initial data. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 71. doi : 10.1051/mmnp/2020030. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020030/

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