The Barenblatt – Zheltov – Kochina model with additive white noise in quasi-Sobolev spaces

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".