The Barenblatt - Zheltov - Kochina Model on The Segment with Wentzell Boundary Conditions

Abstract

In terms of the theory of relative p-bounded operators, we study the Barenblatt– Zheltov–Kochina model, which describes dynamics of pressure of a filtered fluid in a fractured-porous medium with general Wentzell boundary conditions. In particular, we consider spectrum of one-dimensional Laplace operator on the segment [0, 1] with general Wentzell boundary conditions. We examine the relative spectrum in one-dimensional Barenblatt–Zheltov–Kochina equation, and construct the resolving group in the CauchyWentzell problem with general Wentzell boundary conditions. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space L 2 (0, 1).