# Кафедра математики

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### Browsing Кафедра математики by Author "Drin, Iryna"

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Item The analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument(2023) Drin, Yaroslav; Drin, Iryna; Drin, SvitlanaIn 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.Item The cauchy problem for quasilinear equation with nonstationary diffusion coefficient(2023) Drin, Yaroslav; Drin, Iryna; Drin, SvitlanaThe initial problem for the heat conduction equation with the inversion of the argument are considered and Green’s function are determined. The theorem declared that the Poisson’s formula determines the solution of the Cauchy problem considered and proved.Item The first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument(2022) Drin, Yaroslav; Drin, Iryna; Drin, Svitlana; Stetsko, YuriyThe initial-boundary problem for the heat conduction equation with the inversion of the argument are considered. The Green’s function of considered problem are determined. The theorem about the Poisson integral limitation is proved. The theorem declared that the Poisson integral determine the solution of the first boundary problem considered and proved.