The article considers the Aller Lykov equation with a Riemann Liouville fractional time derivative, boundary conditions of the third kind and with the concentrated specific heat capacity on the boundary of the domain. Similar conditions arise in the case with a material of a higher thermal conductivity when solving a temperature problem for restricted environment with a heater as a concentrated heat capacity. Analogous conditions also arise in practices for regulating the water-salt regime of soils, when desalination of the upper layer is achieved by draining of a surface of the flooded for a while area. Using energy inequality methods, we obtained an a priori estimate in terms of the Riemann Liouville fractional derivative, which revealed the uniqueness of the solution to the problem under consideration.

Работа посвящена исследованию локально-одномерных схем для уравнения теплопроводности с нестационарным краевым условием, когда на границе области помещена сосредоточенная теплоемкость некоторой величины. В работе получена априорная оценка в равномерной метрике, откуда следует сходимость построенной схемы на кубической сетке.

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In this paper a modification of the local variation method for minimizing the elasticity functionals, which reduces the counting time when varying them with small steps is proposed. Example of the solution of the inverse problem of the theory of elasticity by the finite element method is given. The problem of finding the elastic characteristics of a three-layer cable insulation, in which the annular stresses and deformations practically do not vary radially, is solved.

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