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Short Notes

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

N. S. Goncharov

South Ural State University, Chelyabinsk, Russian Federation

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 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 $L^2(0,1)$.

Keywords: Barenblatt–Zheltov–Kochina model, relatively p-bounded operator, phase space, $C_0$-contraction semigroups, Wentzell boundary conditions.

UDC: 517.9

MSC: 35G15

Received: 03.02.2019

Language: English

DOI: 10.14529/mmp190211

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