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Journal Articles Mathematical Modelling of Natural Phenomena Year : 2020

On the maximization problem for solutions of reaction–diffusion equations with respect to their initial data

Abstract

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.
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Dates and versions

hal-03039668 , version 1 (05-07-2019)
hal-03039668 , version 2 (04-12-2020)

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Cite

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, 2020, 15, pp.71. ⟨10.1051/mmnp/2020030⟩. ⟨hal-03039668v2⟩
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