MULTIPOINT INITIAL-FINAL VALUE PROBLEM FOR THE MODEL OF DEVIS WITH ADDITIVE WHITE NOISE

Abstract

The evolution of the free surface of the ltering uid 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 dierent initial (initial-nal value conditions). The stochastic model is studied for the rst time. The main result is the proof of the unique solvability of the evolutionary model with an additive white noise and a multipoint initial-nal value condition