Journal
INVERSE PROBLEMS
Volume 35, Issue 10, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/ab1c69
Keywords
inverse coefficient problem; transport equation; stability; local Carleman estimate
Categories
Funding
- Japan Society for the Promotion of Science [15H05740]
- NSFC [11771270, 91730303]
- RUDN University Program 5-100
- Japan Society for the Promotion of Science
- University of Rome 'Tor Vergata'
- Istituto Nazionale di Alta Matematica (INdAM), through the GNAMPA Research Project 2017 'Comportamento asintotico e controllo di equazioni di evoluzione non lineari'
- research project of the Universita di Napoli Federico II: 'Spectral and Geometrical Inequalities'
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We consider the transport equation partial derivative(t)u(x, t) + (H(x) . del u(x, t)) + p(x)u(x, t) = 0 in Omega x (0, T) where Omega subset of R-n is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function H(x) or a real-valued function p(x) by initial values and data on a subboundary of Omega. Our results are conditional stability of Holder type in a subdomain D provided that the outward normal component of H(x) is positive on partial derivative D boolean AND partial derivative Omega. The proofs are based on a Carleman estimate where the weight function depends on H.
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