Geodesic
The Barenblatt--Zheltov--Kochina equation with boundary Neumann condition and multipoint initial-final value condition
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 11 (2019) no. 2, pp. 14-19

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The article is devoted to the study of the unique solvability of the Barenblatt–Zheltov–Kochina equation, equipped with the Neumann boundary condition and a multipoint initial-final value condition. This equation is degenerate or, in other words, it belongs to the Sobolev type equations. To study this equation, the authors used the methods of the theory of degenerate operator semigroups, created by Prof. G.A. Sviridyuk, and further developed by him and his students. We would also like to note that the equation under study is supplied with a multipoint initial-final value condition, which is not just a generalization of the Cauchy problem for the Sobolev type equations. This condition makes it possible to avoid checking the consistency of the initial data when finding a solution.
Keywords: Barenblatt–Zheltov–Kochina equation, multipoint initial-final value condition, unique solvability.
Mots-clés : Neumann condition 
@article{VYURM_2019_11_2_a1,
     author = {L. A. Kovaleva and E. A. Soldatova and S. A. Zagrebina},
     title = {The {Barenblatt--Zheltov--Kochina} equation with boundary {Neumann} condition and multipoint initial-final value condition},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {14--19},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2019_11_2_a1/}
}
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L. A. Kovaleva; E. A. Soldatova; S. A. Zagrebina. The Barenblatt--Zheltov--Kochina equation with boundary Neumann condition and multipoint initial-final value condition. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 11 (2019) no. 2, pp. 14-19. http://geodesic.mathdoc.fr/item/VYURM_2019_11_2_a1/