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Copyright © 2015 A. Favini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The concept of "white noise," initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of "noises" are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable "noises." The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application.

Details

Title
Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of "Noises"
Author
Favini, A; Sviridyuk, G A; Manakova, N A
Publication year
2015
Publication date
2015
Publisher
John Wiley & Sons, Inc.
ISSN
10853375
e-ISSN
16870409
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1744609464
Copyright
Copyright © 2015 A. Favini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.