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Direct and inverse source problems for degenerate parabolic equations

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dc.contributor.authorHussein, M. S.
dc.contributor.authorLesnic, D.
dc.contributor.authorKamynin, V. L.
dc.contributor.authorKostin, A. B.
dc.contributor.authorКамынин, Виталий Леонидович
dc.contributor.authorКостин, Андрей Борисович
dc.date.accessioned2024-11-25T17:27:27Z
dc.date.available2024-11-25T17:27:27Z
dc.date.issued2020
dc.description.abstract© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- A nd time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
dc.identifier.citationDirect and inverse source problems for degenerate parabolic equations / Hussein, M.S. [et al.] // Journal of Inverse and Ill-Posed Problems. - 2020. - 10.1515/jiip-2019-0046
dc.identifier.doi10.1515/jiip-2019-0046
dc.identifier.urihttps://www.doi.org/10.1515/jiip-2019-0046
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85082316828&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000561130900009
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/20476
dc.relation.ispartofJournal of Inverse and Ill-Posed Problems
dc.titleDirect and inverse source problems for degenerate parabolic equations
dc.typeArticle
dspace.entity.typePublication
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