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2015 Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
A. Favini, G. A. Sviridyuk, N. A. Manakova
Abstr. Appl. Anal. 2015: 1-8 (2015). DOI: 10.1155/2015/697410

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.

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A. Favini. G. A. Sviridyuk. N. A. Manakova. "Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”." Abstr. Appl. Anal. 2015 1 - 8, 2015. https://doi.org/10.1155/2015/697410

Information

Published: 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1345.60054
MathSciNet: MR3431491
Digital Object Identifier: 10.1155/2015/697410

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
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