We consider the transport equation ∂tu(x,t)+(H(x) - ∇u(x,t))+p(x)u(x,t)=0 in Ω ×(0,t) where Ω ⊂ ℝn is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function p(x) or a real-valued function Ω by initial values and data on a subboundary of Ω. Our results are conditional stability of Hölder type in a subdomain D provided that the outward normal component of H(x) is positive on ∂D∩∂Ω. The proofs are based on a Carleman estimate where the weight function depends on H.
Inverse coefficient problems for a transport equation by local Carleman estimate / Cannarsa, P.; Floridia, G.; Golgeleyen, F.; Yamamoto, M.. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 35:10(2019). [10.1088/1361-6420/ab1c69]
Inverse coefficient problems for a transport equation by local Carleman estimate
Cannarsa P.;Floridia G.;
2019
Abstract
We consider the transport equation ∂tu(x,t)+(H(x) - ∇u(x,t))+p(x)u(x,t)=0 in Ω ×(0,t) where Ω ⊂ ℝn is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function p(x) or a real-valued function Ω by initial values and data on a subboundary of Ω. Our results are conditional stability of Hölder type in a subdomain D provided that the outward normal component of H(x) is positive on ∂D∩∂Ω. The proofs are based on a Carleman estimate where the weight function depends on H.| File | Dimensione | Formato | |
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CFGY Arxiv 1902.06355.pdf
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