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Application of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions

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dc.contributor.authorKostin, A. B.
dc.contributor.authorSherstyukov, V. B.
dc.contributor.authorКостин, Андрей Борисович
dc.date.accessioned2024-12-27T09:22:03Z
dc.date.available2024-12-27T09:22:03Z
dc.date.issued2023
dc.description.abstractUsing an example of the Cauchy problem for the one-dimensional heat equation, we study the approximation of the solution to the initial condition in the Hausdorff metric. The simplest discontinuous function u0(x) = sgn x is taken for the initial condition. Based on the asymptotic behavior of the Lambert W function and its modification, we obtain a two-sided estimate and an asymptotics for the Hausdorff distance between the solution given by the Poisson formula and the function u0(x). Similar results are obtained for a similar model problem for the Laplace equation in the upper half-plane.
dc.identifier.citationKostin, A. B. Application of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions / Kostin, A. B., Sherstyukov, V. B. // Journal of Mathematical Sciences (United States). - 2023. - 10.1007/s10958-023-06616-6
dc.identifier.doi10.1007/s10958-023-06616-6
dc.identifier.urihttps://www.doi.org/10.1007/s10958-023-06616-6
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85168603937&origin=resultslist
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/29205
dc.relation.ispartofJournal of Mathematical Sciences (United States)
dc.subjectHausdorff distance
dc.subjectPoisson s equation
dc.subjectBoundary Element Method
dc.titleApplication of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication3070740c-c832-420c-a070-a880195523bc
relation.isAuthorOfPublication.latestForDiscovery3070740c-c832-420c-a070-a880195523bc
relation.isOrgUnitOfPublicationd19559ab-04cd-486a-ae8e-f40ccd36a1a6
relation.isOrgUnitOfPublication.latestForDiscoveryd19559ab-04cd-486a-ae8e-f40ccd36a1a6
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