Stochastic devis model whith multipoint initial-final value

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-nal value conditions). The stochastic model is studied here. Several approaches to solving this problems are mentioned, differing y their understanding of the “white noise”. The definition of a solution is given, as well as definitions os the used stochastic processes. The solvability of the multipoint initial-finite problem for the stochastic Davis model is given in the article. The main result is the proof of the unique solvability of the evolutionary model with an additive white noise and a multipoint initial-final condition using linear algebra and spectral methods.