The Barenblatt - Zheltov - Kochina Model with Additive White Noise in Quasi-Sobolev Spaces
Copyright policy )The Barenblatt - Zheltov - Kochina Model with Additive White Noise in Quasi-Sobolev Spaces
Summary: 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''.
- South Ural State University Russian Federation
Operator theory in probabilistic metric linear spaces, Applications of stochastic analysis (to PDEs, etc.), White noise theory, stochastic Sobolev-type equations, Wiener process, Nelson-Gliklikh derivative, quasi-Sobolev spaces, Barenblatt-Zheltov-Kochina stochastic equation, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, white noise
Operator theory in probabilistic metric linear spaces, Applications of stochastic analysis (to PDEs, etc.), White noise theory, stochastic Sobolev-type equations, Wiener process, Nelson-Gliklikh derivative, quasi-Sobolev spaces, Barenblatt-Zheltov-Kochina stochastic equation, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, white noise
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