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Pré-Publication, Document De Travail Année : 2021

Optimal control of a first order Fokker-Planck equation with reaction term and density constraints

Résumé

We consider a constrained optimal control of an advection-reaction partial differential equation (PDE). We prove the existence of a minimizer and we characterize the solution as the weak solution of a system of two coupled PDEs. This system is composed of a Fokker-Planck equation and of a Hamilton-Jacobi equation, similarly to systems obtained in Mean Field Games (MFG). We provide regularity results of the solutions.
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Dates et versions

hal-03353917 , version 1 (24-09-2021)
hal-03353917 , version 2 (18-10-2021)
hal-03353917 , version 3 (26-10-2022)
hal-03353917 , version 4 (24-01-2024)

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Citer

Adrien Seguret. Optimal control of a first order Fokker-Planck equation with reaction term and density constraints. 2021. ⟨hal-03353917v2⟩
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