{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T13:26:20Z","timestamp":1770729980252,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003336","name":"Bulgarian National Science Fund","doi-asserted-by":"publisher","award":["KP-06-N 62\/3"],"award-info":[{"award-number":["KP-06-N 62\/3"]}],"id":[{"id":"10.13039\/501100003336","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The third-order pseudoparabolic equations represent models of filtration, the movement of moisture and salts in soils, heat and mass transfer, etc. Such non-classical equations are often referred to as Sobolev-type equations. We consider an inverse problem for identifying an unknown time-dependent boundary condition in a two-dimensional linear pseudoparabolic equation from integral-type measured output data. Using the integral measurements, we reduce the two-dimensional inverse problem to a one-dimensional problem. Then, we apply appropriate substitution to overcome the non-local nature of the problem. The inverse ill-posed problem is reformulated as a direct well-posed problem. The well-posedness of the direct and inverse problems is established. We develop a computational approach for recovering the solution and unknown boundary function. The results from numerical experiments are presented and discussed.<\/jats:p>","DOI":"10.3390\/computation12120243","type":"journal-article","created":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T12:58:49Z","timestamp":1733921929000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Numerical Determination of a Time-Dependent Boundary Condition for a Pseudoparabolic Equation from Integral Observation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0360-3651","authenticated-orcid":false,"given":"Miglena N.","family":"Koleva","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences and Education, \u201cAngel Kanchev\u201d University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria"}]},{"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, \u201cAngel Kanchev\u201d University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124533","DOI":"10.1016\/j.jmaa.2020.124533","article-title":"Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media","volume":"493","author":"Amar","year":"2021","journal-title":"J. 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