The Barenblatt–Zheltov–Kochina Equation with Boundary Neumann Condition and Multipoint Initial-Final Value Condition

Lyudmila Aleksandrovna Kovaleva; Ekaterina Aleksandrovna Soldatova; Sof'ya Aleksandrovna Zagrebina

doi:10.14529/mmph190202

Авторы

Lyudmila Aleksandrovna Kovaleva South Ural State University, Chelyabinsk
Ekaterina Aleksandrovna Soldatova South Ural State University, Chelyabinsk
Sof'ya Aleksandrovna Zagrebina South Ural State University, Chelyabinsk

DOI:

https://doi.org/10.14529/mmph190202

Ключевые слова:

Barenblatt–Zheltov–Kochina equation, Neumann condition, multipoint initial-final value condition, unique solvability

Аннотация

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.