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- W3153577445 abstract "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." @default.
- W3153577445 created "2021-04-26" @default.
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- W3153577445 date "2023-01-01" @default.
- W3153577445 modified "2023-09-25" @default.
- W3153577445 title "Boundary control for transport equations" @default.
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- W3153577445 doi "https://doi.org/10.3934/mcrf.2022014" @default.
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