Boundary Control for Transport Equations
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Boundary Control for Transport Equations
Author(s) :
Bal, Guillaume [Auteur]
University of Chicago
Jollivet, Alexandre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
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
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 >
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
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Non
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