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THE INVERSE PROBLEM OF DETERMINING THE LOWEST COEFFICIENT IN A HIGHER-ORDER PARABOLIC EQUATION WITH WEAK DEGENERACY

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dc.contributor.authorKamynin, V. L.
dc.contributor.authorKostin, A. B.
dc.contributor.authorКамынин, Виталий Леонидович
dc.contributor.authorКостин, Андрей Борисович
dc.date.accessioned2024-11-29T21:07:07Z
dc.date.available2024-11-29T21:07:07Z
dc.date.issued2021
dc.description.abstractWe consider the inverse problem of finding the coefficient before u(t, x) in a higher-order parabolic equation, which is not assumed to be uniformly parabolic and can admit weak degeneracy. The required coefficient is considered to depend only on the spatial variable x is an element of [0, l]. Additional information is taken in the form of an integral over the variable t is an element of [0, T] of the solution with a given weight function (integral observation). The initial condition and m boundary conditions of the first kind (2m order of the equation) are specified in a standard way. It is assumed that the leading coefficient rho before u(t) in the equation is non-negative, and its reciprocal 1/rho belongs to the space L-q(Q) for some q > 1. For the considered inverse problem, existence and uniqueness theorems for the generalized solution are proved. In the course of its research, the corresponding theorems on the solvability of the direct problem were formulated and proved. In this case, the approaches and results of the well-known work of S. N. Kruzhkov(1979) were used. In the conclusion, we give an example of the inverse problem for which the conditions of the theorems proved are satisfied. It is shown that for all sufficiently large values of T > 0 its solution exists, is unique, and an estimate for the required coefficient is written out.
dc.format.extentС. 53-67
dc.identifier.citationKamynin, V. L. THE INVERSE PROBLEM OF DETERMINING THE LOWEST COEFFICIENT IN A HIGHER-ORDER PARABOLIC EQUATION WITH WEAK DEGENERACY / Kamynin, VL, Kostin, AB // Eurasian Journal of Mathematical and Computer Applications. - 2021. - 9. - № 3. - P. 53-67. - 10.32523/2306-6172-2021-9-3-53-67
dc.identifier.doi10.32523/2306-6172-2021-9-3-53-67
dc.identifier.urihttps://www.doi.org/10.32523/2306-6172-2021-9-3-53-67
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85118615465&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000702357700005
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/24774
dc.relation.ispartofEurasian Journal of Mathematical and Computer Applications
dc.titleTHE INVERSE PROBLEM OF DETERMINING THE LOWEST COEFFICIENT IN A HIGHER-ORDER PARABOLIC EQUATION WITH WEAK DEGENERACY
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue3
oaire.citation.volume9
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relation.isAuthorOfPublication3070740c-c832-420c-a070-a880195523bc
relation.isAuthorOfPublication.latestForDiscovery79800a27-7e0d-4efe-834f-93de0b11dd09
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