Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2026, Volume: 67, Number: 2, Pages: 350-356 Pages count : 7 DOI: 10.1134/s0037446626020084 | ||
| Tags | parabolic equation, cauchy problem, structure of the solution, tomography, inverse problem, uniqueness | ||
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0029 |
Abstract:
For an equation of parabolic type whose principal part is the heat operator, we study the Cauchy problem with a point source. A special structure of the solution to this problem is written out. It is based on a representation of the solution as the product of the fundamental solution to the heat equation and a polynomial in powers of t with coefficients depending on the spatial variables. Formulas for computing these coefficients are derived, and an estimate of the remainder term is given. Next, two inverse problems for the original equation are posed. They are then studied on the basis of the obtained structure of the solution to the Cauchy problem. A uniqueness theorem is formulated for the considered inverse problems.
Cite:
Romanov V.G.
Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems
Siberian Mathematical Journal. 2026. V.67. N2. P.350-356. DOI: 10.1134/s0037446626020084 РИНЦ OpenAlex
Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems
Siberian Mathematical Journal. 2026. V.67. N2. P.350-356. DOI: 10.1134/s0037446626020084 РИНЦ OpenAlex
Dates:
| Submitted: | Dec 31, 2025 |
| Accepted: | Jan 26, 2026 |
| Published online: | Mar 28, 2026 |
Identifiers:
| ≡ Elibrary: | 89161335 |
| ≡ OpenAlex: | W7141916289 |