THE BARENBLATT -- ZHELTOV -- KOCHINA MODEL WITH ADDITIVE WHITE NOISE IN QUASI-SOBOLEV SPACES

Abstract

In order to carry over the theory of linear stochastic Sobolev-type equations to quasi-Banach spaces, we construct a~space of differentiable quasi-Sobolev "noises" and establish the existence and uniqueness of a~classical solution to the Showalter -- Sidorov problem for a stochastic Sobolev-type equation with a relatively $p$-bounded operator. Basing on the abstract results, we study the Barenblatt -- Zheltov -- Kochina stochastic model with the Showalter--Sidorov initial condition in quasi-Sobolev spaces with an~external action in the form of "white noise"