The Barenblatt–Zheltov–Kochina model on the segment with Wentzell boundary conditions

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 Cauchy-Wentzell 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 $L^2(0,1)$.