The cauchy problem for one class of parabolic pseudodifferential equation with deviation of the argument

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dc.contributor.authorDrin, Yaroslav en_US
dc.contributor.authorDrin, Iryna en_US
dc.contributor.authorDrin, Svitlana en_US
dc.contributor.authorKotsur, Maksym en_US
dc.date.accessioned2025-11-05T13:44:55Z
dc.date.available2025-11-05T13:44:55Z
dc.date.issued2015
dc.description.abstractIn this paper, we study solvability of the Cauchy problem for a parabolic pseudodifferential equation with the deviation of the argument. Parabolic pseudodifferential operator with non-smooth symbols introduced by Eidel’man and Drin’ for the first time. For such equations, the initial condition is set on a certain interval. Technical and physical reasons for delays can be transport delays, delays in decision-making, delays in information transmission, etc. The most natural are delays when modeling objects in medicine, population dynamics, ecology, etc. Other physical and technical interpretations are also possible, for example, the molecular distribution of thermal energy in various media (liquids, solid bodies, etc.) is modeled by heat conduction equations. Features of the dynamics of vehicles in different environments (water, land, air) can also be taken into account by introducing a delay. The formula for the solution of the Cauchy problem is constructed for the nonlinear equation of heat conduction with a deviation of the argument, its properties are investigated. en_US
dc.identifier.citationThe cauchy problem for one class of parabolic pseudodifferential equation with deviation of the argument / Yaroslav M. Drin, Iryna I. Drin, Svitlana S. Drin, Maksym P. Kotsur // Journal of Optimization Differential Equations and their Applications. - 2025. - Vol. 33, Issue 1. - P. 208-220. - https://doi.org/10.15421/142510 en_US
dc.identifier.issn2312-4547
dc.identifier.issn2415-7325
dc.identifier.urihttps://doi.org/10.15421/142510
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/37395
dc.language.isoen en_US
dc.relation.sourceJournal of Optimization Differential Equations and their Applications en_US
dc.statusfirst published en_US
dc.subjectpseudodifferential nonlinear equation en_US
dc.subjectCauchy problem en_US
dc.subjectdeviation argument en_US
dc.subjectstep method en_US
dc.subjectarticle en_US
dc.titleThe cauchy problem for one class of parabolic pseudodifferential equation with deviation of the argument en_US
dc.typeArticle en_US
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