Volume 12, no. 2Pages 136 - 142

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

N.S. Goncharov
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).
Full text
Barenblatt-Zheltov-Kochina model; relatively p-bounded operator; phase space; C0-contraction semigroups; Wentzell boundary conditions.
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