{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T23:05:43Z","timestamp":1762643143127,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["FENG-2023-0004"],"award-info":[{"award-number":["FENG-2023-0004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study inverse problems of identification of lower-order coefficients in a second-order parabolic equation. The coefficients are sought in the form of a finite series segment with unknown coefficients, depending on time. The linear case is also considered. Overdetermination conditions are the integrals over the boundary of a solution\u2019s domain with weights. We focus on existence and uniqueness theorems and stability estimates for solutions to these inverse problems. An operator equation to which the problem is reduced is studied with the use of the contraction mapping principle. A solution belongs to some Sobolev space and has all generalized derivatives occurring into the equation summable to some power. The method of the proof is constructive, and it can be used for developing new numerical algorithms for solving the problem.<\/jats:p>","DOI":"10.3390\/axioms14020116","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T04:36:51Z","timestamp":1738557411000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inverse Problems of Recovering Lower-Order Coefficients from Boundary Integral Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7238-9559","authenticated-orcid":false,"given":"Sergey","family":"Pyatkov","sequence":"first","affiliation":[{"name":"Engineering School of Digital Technologies, Yugra State University, Chekhov St. 16, 628011 Khanty-Mansiysk, Russia"},{"name":"Academy of Sciences of the Republic of Sakha (Yakutia), 33 Lenin Ave., 677007 Yakutsk, Russia"}]},{"given":"Oleg","family":"Soldatov","sequence":"additional","affiliation":[{"name":"Engineering School of Digital Technologies, Yugra State University, Chekhov St. 16, 628011 Khanty-Mansiysk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,1]]},"reference":[{"key":"ref_1","unstructured":"Alifanov, O.M., Artyukhin, E.A., and Nenarokomov, A.V. (2009). Inverse Problems in the Study of Complex Heat Transfer, Janus-K."},{"key":"ref_2","unstructured":"Ozisik, M.N., and Orlande, H.R.B. (2000). Inverse Heat Transfer, Taylor & Francis."},{"key":"ref_3","unstructured":"Prilepko, A.I., Orlovsky, D.G., and Vasin, I.A. (1999). Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Belov, Y.Y. (2002). Inverse Problems for Parabolic Equations, VSP.","DOI":"10.1515\/9783110944631"},{"key":"ref_5","unstructured":"Isakov, V. (2006). Inverse Problems for Partial Differential Equations, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kabanikhin, S.I. (2012). Inverse and III-Posed Problems, Walter de Gruyter.","DOI":"10.1515\/9783110224016"},{"key":"ref_7","first-page":"139","article-title":"On Solving an Inverse Problem for a Multidimensional Parabolic Equation","volume":"15","author":"Frolenkov","year":"2012","journal-title":"Sib. J. Ind. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"287","DOI":"10.3103\/S1055134412040050","article-title":"On Some Classes of Coefficient Inverse Problems for Parabolic Systems of Equations","volume":"22","author":"Pyatkov","year":"2012","journal-title":"Sib. Adv. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s00028-010-0087-6","article-title":"On Some Classes of Inverse Problems for Parabolic and Elliptic Equations","volume":"11","author":"Pyatkov","year":"2011","journal-title":"J. Evol. Eq."},{"key":"ref_10","first-page":"917","article-title":"On Some Classes of Inverse Problems for Parabolic Equations","volume":"18","author":"Pyatkov","year":"2011","journal-title":"J. Inv. III-Posed Probl."},{"key":"ref_11","first-page":"1515","article-title":"On Some Problems of the Reconstruction of a Boundary Condition for a Parabolic Equation, II","volume":"32","author":"Kostin","year":"1996","journal-title":"Differ. Eq."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1134\/S0037446616050177","article-title":"On Some Classes of Inverse Problems with Overdetermination Data on Spatial Manifolds","volume":"57","author":"Pyatkov","year":"2016","journal-title":"Sib. Math. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"124","DOI":"10.3103\/S1055134420020054","article-title":"On some parabolic inverse problems with the pointwise overdetermination","volume":"30","author":"Pyatkov","year":"2020","journal-title":"Siber. Adv. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"52","DOI":"10.14529\/jcem220205","article-title":"Identification of Thermophysical Parameters in Mathematical Models of Heat and Mass Transfer","volume":"9","author":"Pyatkov","year":"2022","journal-title":"J. Comput. Eng. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"020008","DOI":"10.1063\/1.5012619","article-title":"Inverse Problems with Pointwise Overdetermination for some Quasilinear Parabolic Systems","volume":"1907","author":"Pyatkov","year":"2017","journal-title":"AIP Conf. Proc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s10958-023-06593-w","article-title":"Inverse problems of recovering the heat transfer coefficient with integral data","volume":"274","author":"Pyatkov","year":"2023","journal-title":"J. Math. Sci."},{"key":"ref_17","first-page":"264","article-title":"Linear Inverse Problems for Some Classes of Nonlinear Nonstationary Equations","volume":"12","author":"Kozhanov","year":"2015","journal-title":"Sib. Electron. Rep."},{"key":"ref_18","first-page":"3","article-title":"On Some Inverse Problems of Recovering Boundary Regimes","volume":"23","author":"Verzhbitskiy","year":"2016","journal-title":"Math. Notes NEFU"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"095020","DOI":"10.1088\/0266-5611\/29\/9\/095020","article-title":"Determination of the Heat Transfer Coefficients in Transient Heat Conduction","volume":"29","author":"Dihn","year":"2013","journal-title":"Inverse Probl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1080\/00036811.2014.948425","article-title":"Identification of Nonlinear Heat Transfer Laws from Boundary Observations","volume":"94","author":"Hao","year":"2014","journal-title":"Appl. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1080\/00036810500384136","article-title":"Identifying a Spherically Symmetric Conductivity in a Nonlinear Parabolic Equation","volume":"85","author":"Lorenzi","year":"2006","journal-title":"Appl. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1080\/15502287.2016.1231241","article-title":"Simultaneous Determination of Time-Dependent Coefficients and Heat Source","volume":"17","author":"Hussein","year":"2016","journal-title":"Intern. J. Comput. Methods Eng. Sci. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4918256","DOI":"10.1155\/2018\/4918256","article-title":"Identification of a Time-Dependent Coefficient in Heat Conduction Problem by New Iteration Method","volume":"2018","author":"Huang","year":"2018","journal-title":"Adv. Math. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.5194\/gmd-11-2009-2018","article-title":"Soil Methanotrophy Model (MeMo v1.0): A Process-Based Model to Quantify Global Uptake of Atmospheric Methane by Soil","volume":"11","author":"Arndt","year":"2018","journal-title":"Geosci. Model Dev."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Samarskii, A.A., and Vabishchevich, P.N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics, Walter de Gruyter GmbH & Co. KG.","DOI":"10.1515\/9783110205794"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1080\/17415977.2020.1814282","article-title":"Identification of the Timewise Thermal Conductivity in a 2D Heat Equation from Local Heat Flux Conditions","volume":"29","author":"Huntul","year":"2021","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1134\/S0037446624040104","article-title":"Identification of the Heat Transfer Coefficient from Boundary Integral Data","volume":"65","author":"Pyatkov","year":"2024","journal-title":"Sib. Math. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10958-024-07346-z","article-title":"Coefficient Inverse Problems of Identification of Thermophysical Parameters from Boundary Integral Data","volume":"282","author":"Pyatkov","year":"2024","journal-title":"J. Math. Sci."},{"key":"ref_29","unstructured":"Triebel, H. (1978). Interpolation Theory. Function Spaces. Differential Operators, VEB Deutscher Verlag der Wissenschaften."},{"key":"ref_30","first-page":"161","article-title":"Compact embeddings of vector-valued sobolev and besov spaces","volume":"35","author":"Amann","year":"2000","journal-title":"Glas. Mat."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Amann, H. (1995). Linear and Quasilinear Parabolic Problems, Birkhauser Verlag.","DOI":"10.1007\/978-3-0348-9221-6"},{"key":"ref_32","unstructured":"Ladyzhenskaya, O.A., Solonnikov, V.A., and Uraltseva, N.N. (1968). Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society."},{"key":"ref_33","first-page":"38","article-title":"On some classes of inverse problems with pointwise ovedetermination for mathematical models of heat and mass transfer","volume":"3","author":"Baranchuk","year":"2020","journal-title":"Bull. Yugra State Univ."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/116\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:25:39Z","timestamp":1760027139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,1]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020116"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020116","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,2,1]]}}}