Geodesic
The Barenblatt – Zheltov – Kochina model with additive white noise in quasi-Sobolev spaces
Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 61-67

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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".
Keywords: Sobolev-type equations; Wiener process; Nelson – Gliklikh derivative; white noise; quasi-Sobolev spaces; Barenblatt – Zheltov – Kochina stochastic equation. 
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     author = {G. A. Sviridyuk and N. A. Manakova},
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G. A. Sviridyuk; N. A. Manakova. The Barenblatt – Zheltov – Kochina model with additive white noise in quasi-Sobolev spaces. Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 61-67. http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a6/