stochastic Dzekzer equation, system of Wentzell equations, the Nelson–Glicklich derivative
Abstract
Deterministic and stochastic Wentzell systems of the Dzekzer equations describing the evolution of the free surface of a filtering fluid in a hemisphere and at its edge are studied. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a particular constructed Hilbert space is established. In the case of the stochastic system, the theory of Nelson–Glicklich derivatives is used and a stochastic solution is constructed to quantify the change in the free filtration of the fluid.
Author Biographies
Nikita Sergeevich Goncharov, South Ural State University, Chelyabinsk
Post-graduate Student, Equations of Mathematical Physics Department
Georgiy Anatol'evich Sviridyuk, South Ural State University, Chelyabinsk
Professor, Dr. Sc. (Physics and Mathematics), Head of Mathematical Physics Non-Classical Equations Research Laboratory
