Analysis of the system of Wentzell equations in the circle and on its boundary

In this paper the system of Wentzell equations, which is represented by two differential equations, namely, the Barenblatt – Zheltov – Kochina equation describing the heat conduction process at two temperatures inside a circle with the dynamic boundary condition ofWentzel, represented as a heat conduction equation with the Laplace – Beltrami operator, set on the boundary of the circle. Meanwhile, in the classical theory of boundary value problems, the boundary condition is understood as an equation on the boundary in which the order of derivatives on spatial variables is at least one less than the order of derivatives in the equation given in the domain. Therefore the study of Wentzell’s system of equations opens the door to a new direction in research, where the equations can have derivatives of any order on both spatial and temporal variables.