Stochastic Barenblatt–Zheltov–Kochina model with Neumann condition and multipoint initial-final value condition

The article deals with the stochastic Barenblatt–Zheltov–Kochina model with the Neumann condition. We prove trajectory-wise unique solvability of the multipoint initial-final value problem for the considered model in the domain. The article, in addition to the introduction and references, contains three parts. The first and second parts present theoretical information about deterministic and stochastic equations of Sobolev type with the multipoint initial-final value condition. The third part examines the solvability of the Bareblatt–Zheltov–Kochina model with the Neumann condition and the initial-final value condition.