Inverse coefficient problems for a transport equation by local Carleman estimate

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. © 2019 IOP Publishing Ltd.

Authors
Cannarsa P.1 , Floridia G.2 , Gölgeleyen F.3 , Yamamoto M. 4, 5, 6
Publisher
Institute of Physics Publishing
Number of issue
10
Language
English
Status
Published
Number
105013
Volume
35
Year
2019
Organizations
  • 1 Department of Mathematics, University of Rome 'Tor Vergata', ROME, 00133, Italy
  • 2 Department of Mathematics and Applications 'R. Caccioppoli', University of Naples Federico II, Naples, 80126, Italy
  • 3 Department of Mathematics, Faculty of Arts and Sciences, Zonguldak Bulent Ecevit University, Zonguldak, 67100, Turkey
  • 4 Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153, Japan
  • 5 Academy of Romanian Scientists, Splaiul Independentei, Street no 54, Bucharest, 050094, Romania
  • 6 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Inverse coefficient problem; Local Carleman estimate; Stability; Transport equation
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55018/