Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”

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-...

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Main Authors:	A. Favini, G. A. Sviridyuk, N. A. Manakova
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2015/697410

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spelling	doaj-e5b86af116304f4299ba108dec5c0d862020-11-24T20:40:23ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/697410697410Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”A. Favini0G. A. Sviridyuk1N. A. Manakova2Department of Mathematics, University of Bologna, 5 Piazza di Porta San Donato, 40126 Bologna, ItalyDepartment of Mathematics, Mechanics and Computer Sciences, South Ural State University, 76 Lenin Avenue, Chelyabinsk 454080, RussiaDepartment of Mathematics, Mechanics and Computer Sciences, South Ural State University, 76 Lenin Avenue, Chelyabinsk 454080, RussiaThe 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.http://dx.doi.org/10.1155/2015/697410
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A. Favini G. A. Sviridyuk N. A. Manakova
spellingShingle	A. Favini G. A. Sviridyuk N. A. Manakova Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises” Abstract and Applied Analysis
author_facet	A. Favini G. A. Sviridyuk N. A. Manakova
author_sort	A. Favini
title	Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
title_short	Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
title_full	Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
title_fullStr	Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
title_full_unstemmed	Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
title_sort	linear sobolev type equations with relatively p-sectorial operators in space of “noises”
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2015-01-01
description	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.
url	http://dx.doi.org/10.1155/2015/697410
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Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”

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