The analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument

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dc.contributor.authorDrin, Yaroslaven_US
dc.contributor.authorDrin, Irynaen_US
dc.contributor.authorDrin, Svitlanaen_US
dc.date.accessioned2024-10-22T08:43:16Z
dc.date.available2024-10-22T08:43:16Z
dc.date.issued2023
dc.description.abstractIn this article, for the first time, the first boundary value problem for the equation of thermal conductivity with a variable diffusion coefficient and with a nonlinear term, which depends on the sought function with the deviation of the argument, is solved. For such equations, the initial condition is set on a certain interval. Physical and technical reasons for delays can be transport delays, delays in information transmission, delays in decision-making, etc. The most natural are delays when modeling objects in ecology, medicine, population dynamics, etc. Features of the dynamics of vehicles in different environments (water, land, air) can also be taken into account by introducing a delay. Other physical and technical interpretations are also possible, for example, the molecular distribution of thermal energy in various media (solid bodies, liquids, etc.) is modeled by heat conduction equations. The Green’s function of the first boundary value problem is constructed for the nonlinear equation of heat conduction with a deviation of the argument, its properties are investigated, and the formula for the solution is established.en_US
dc.identifier.citationDrin Ya. The analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument / Yaroslav Drin, Iryna Drin, Svitlana Drin // Journal of Optimization, Differential Equations and their Applications. - 2023. - Vol. 31, Issue 2. - P. 115-124. - https://doi.org/10.15421/1423013en_US
dc.identifier.issn2617-0108
dc.identifier.issn2663–6824
dc.identifier.urihttps://doi.org/10.15421/1423013
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/31921
dc.language.isoenen_US
dc.relation.sourceJournal of Optimization, Differential Equations and their Applicationsen_US
dc.statusfirst publisheden_US
dc.subjectheat nonlinear equationen_US
dc.subjectboundary value problemen_US
dc.subjectGreen’s functionen_US
dc.subjectdeviation argumenten_US
dc.subjectarticleen_US
dc.titleThe analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argumenten_US
dc.typeArticleen_US
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