On the solvability of the inverse problems of parameter recovery in elliptic equations Full article
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Математические заметки СВФУ (Mathematical Notes of NEFU)
ISSN: 2411-9326 , E-ISSN: 2587-876X |
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| Output data | Year: 2020, Volume: 27, Number: 4, Pages: 14-29 Pages count : 16 DOI: 10.25587/SVFU.2020.57.53.002 | ||||
| Tags | Elliptic equation; Existence; Final-integral overdetermination condition; Regular solution; Uniqueness; Unknown coefficient | ||||
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Abstract:
We study solvability of the inverse problems of finding, alongside the solution u(x, t), the positive parameter a in the differential equations utt + αΔu - Βu = f(x, t), αutt + Δu - Βu = f(x, t) where t ε (0, T), x = (x1,…, xn) ε Ω ⊂ Rn, and Δ the Laplace operator in variables x1,…, xn. As a complement to the boundary conditions defining a well-posed boundary value problem for elliptic equations, we use the conditions of the linear final integral overdetermination. We prove the existence and uniqueness theorems for regular solutions, those having all generalized in the S. L. Sobolev sense derivatives in the equation. © 2020 A. I. Kozhanov.
Cite:
Kozhanov A.I.
On the solvability of the inverse problems of parameter recovery in elliptic equations
Математические заметки СВФУ (Mathematical Notes of NEFU). 2020. V.27. N4. P.14-29. DOI: 10.25587/SVFU.2020.57.53.002 Scopus OpenAlex
On the solvability of the inverse problems of parameter recovery in elliptic equations
Математические заметки СВФУ (Mathematical Notes of NEFU). 2020. V.27. N4. P.14-29. DOI: 10.25587/SVFU.2020.57.53.002 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85101552593 |
| OpenAlex: | W3164782712 |