Inverse coefficient problems for a transport equation by local Carleman estimate
| Autor: | Giuseppe Floridia, Fikret Gölgeleyen, Masahiro Yamamoto, Piermarco Cannarsa |
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| Přispěvatelé: | Cannarsa, P., Floridia, G., Golgeleyen, F., Yamamoto, M., Zonguldak Bülent Ecevit Üniversitesi |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
inverse coefficient problem transport equation stability local Carleman estimate Weight function Applied Mathematics Local Carleman estimate Inverse Function (mathematics) Type (model theory) Domain (mathematical analysis) Computer Science Applications Theoretical Computer Science Combinatorics Transport equation Mathematics - Analysis of PDEs Settore MAT/05 - Analisi Matematica Inverse coefficient problem Bounded function Signal Processing FOS: Mathematics Nabla symbol Convection–diffusion equation Stability Mathematical Physics Analysis of PDEs (math.AP) |
| Popis: | We consider the transport equation $\ppp_tu(x,t) + (H(x)\cdot \nabla u(x,t)) + p(x)u(x,t) = 0$ in $\OOO \times (0,T)$ where $\OOO \subset \R^n$ 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 $\OOO$. Our results are conditional stability of H\"older type in a subdomain $D$ provided that the outward normal component of $H(x)$ is positive on $\ppp D \cap \ppp\OOO$. The proofs are based on a Carleman estimate where the weight function depends on $H$. |
| Databáze: | OpenAIRE |
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