Geodesic
The Barenblatt--Zheltov--Kochina model on the segment with Wentzell boundary conditions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 136-142

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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. 
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     author = {N. S. Goncharov},
     title = {The {Barenblatt--Zheltov--Kochina} model on the segment with {Wentzell} boundary conditions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {136--142},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a10/}
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N. S. Goncharov. The Barenblatt--Zheltov--Kochina model on the segment with Wentzell boundary conditions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 136-142. http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a10/