Boundary Control for Transport Equations

Bal, Guillaume; Jollivet, Alexandre

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.3934/mcrf.2022014

Title :

Boundary Control for Transport Equations

Author(s) :

Bal, Guillaume [Auteur]
University of Chicago
Jollivet, Alexandre [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Mathematical Control and Related Fields

Pages :

721-770

Publisher :

AIMS

Publication date :

2023

ISSN :

2156-8472

English keyword(s) :

Transport theory
boundary control
albedo operator
diffusion approximation
unique continuation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain X can be controlled exactly from incoming boundary conditions ...
Show more >This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain X can be controlled exactly from incoming boundary conditions for X under appropriate convexity assumptions. This is in contrast with the only approximate control one typically obtains for elliptic equations by an application of a unique continuation property, a property which we prove does not hold for transport equations. We also consider the control of an outgoing solution from incoming conditions, a transport notion similar to the Dirichlet-to-Neumann map for elliptic equations. We show that for well-chosen coefficients in the transport equation, this control may not be possible. In such situations and by (Fredholm) duality, we obtain the existence of non-trivial incoming conditions that are compatible with vanishing outgoing conditions.Show less >

Language :

Anglais

Popular science :

Non

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