Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator Full article
| Journal |
Inverse Problems
ISSN: 0266-5611 |
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| Output data | Year: 2019, Volume: 36, Number: 2, Pages: 025003 Pages count : 1 DOI: 10.1088/1361-6420/ab53f3 | ||||
| Tags | Recovering a potential, damped wave equation, subdomains bounded by characteristics, regularity of the solution, uniqueness of the inverse problem solution, Neumann-to-Dirichlet operator, existence of a quasi-solution, Frechet gradient. | ||||
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Abstract:
The inverse coefficient problem of recovering the potential q(x) in the
damped wave equation subject to the boundary conditions r(0)ux(0; t) = f(t), u(l; t) = 0,
from the Dirichlet boundary measured output f(t) := u(0; t), t \in (0; T] is studied.
A detailed microlocal analysis of regularity of the direct problem solution in the
subdomains bounded by the characteristics as well as along these characteristics is
provided. Based on this analysis, necessary regularity results and energy estimates are
derived. It is proved that the Dirichlet boundary measured output uniquely determines
the potential q(x) in the interval [0; h(T=2)] and this solution belongs to C(0; h(T/2)). Moreover, the global uniqueness theorem is proved.
Cite:
Romanov V.
, Hasanov A.
Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator
Inverse Problems. 2019. V.36. N2. P.025003. DOI: 10.1088/1361-6420/ab53f3 WOS Scopus OpenAlex
Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator
Inverse Problems. 2019. V.36. N2. P.025003. DOI: 10.1088/1361-6420/ab53f3 WOS Scopus OpenAlex
Dates:
| Submitted: | Jun 19, 2019 |
| Accepted: | Oct 13, 2019 |
Identifiers:
| Web of science: | WOS:000509242300001 |
| Scopus: | 2-s2.0-85081044092 |
| OpenAlex: | W2986872738 |