This article is cited in 3 papers

Short Notes

Multipoint initial-final value problem for the model of Davis with additive white noise

A. S. Konkina

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The evolution of the free surface of the filtering fluid in a reservoir of limited power is modeled by the Davis equation with homogeneous Dirichlet conditions. Depending on the nature of the free term describing the internal source of the liquid, the model will be deterministic or stochastic. The deterministic model has been studied in various aspects by many researchers with different initial (initial-final value conditions). The stochastic model is studied for the first time. The main result is the proof of the unique solvability of the evolutionary model with an additive white noise and a multipoint initial-final value condition.

Keywords: white noise; Wiener K-process; Davis model; multipoint initial-final value problem; stochastic model.

UDC: 517.9

MSC: 47D06, 35K70

Received: 25.03.2017

Language: English

DOI: 10.14529/mmp170212

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