Stochastic degenerate Sobolev equations: well posedness and exact controllability

Konstantinos B. Liaskos; Ioannis G. Stratis; Athanasios A. Pantelous

doi:10.1002/mma.4077

Stochastic degenerate Sobolev equations: well posedness and exact controllability

Konstantinos B. Liaskos, Ioannis G. Stratis, Athanasios A. Pantelous

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

In this paper, we revisit the recently proposed results for a general class of linear stochastic degenerate Sobolev systems with additive noise by using a different approach keeping, however, the main assumptions unchanged for the purpose of comparison. In particular, the mild and strong well-posedness for the initial and final value problems are presented and studied by applying a suitable transformation that formulates the degenerate stochastic system as a pseudoparabolic one. Based on the derived results for the forward and backward cases, under this new framework, the conditions for the exact controllability are revisited for a particular class of degenerate Sobolev systems.

Original language	English
Pages (from-to)	1025-1032
Number of pages	8
Journal	Mathematical Methods in the Applied Sciences
Volume	41
Issue number	3
DOIs	https://doi.org/10.1002/mma.4077
Publication status	Published - 1 Feb 2018
Externally published	Yes

Keywords

Exact controllability
Singular systems in infinite dimensions
Stochastic backward equations in Hilbert spaces
Stochastic degenerate Sobolev equations

Access to Document

10.1002/mma.4077

Link to publication in Scopus

Cite this

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title = "Stochastic degenerate Sobolev equations: well posedness and exact controllability",

abstract = "In this paper, we revisit the recently proposed results for a general class of linear stochastic degenerate Sobolev systems with additive noise by using a different approach keeping, however, the main assumptions unchanged for the purpose of comparison. In particular, the mild and strong well-posedness for the initial and final value problems are presented and studied by applying a suitable transformation that formulates the degenerate stochastic system as a pseudoparabolic one. Based on the derived results for the forward and backward cases, under this new framework, the conditions for the exact controllability are revisited for a particular class of degenerate Sobolev systems.",

keywords = "Exact controllability, Singular systems in infinite dimensions, Stochastic backward equations in Hilbert spaces, Stochastic degenerate Sobolev equations",

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AU - Liaskos, Konstantinos B.

AU - Stratis, Ioannis G.

AU - Pantelous, Athanasios A.

PY - 2018/2/1

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N2 - In this paper, we revisit the recently proposed results for a general class of linear stochastic degenerate Sobolev systems with additive noise by using a different approach keeping, however, the main assumptions unchanged for the purpose of comparison. In particular, the mild and strong well-posedness for the initial and final value problems are presented and studied by applying a suitable transformation that formulates the degenerate stochastic system as a pseudoparabolic one. Based on the derived results for the forward and backward cases, under this new framework, the conditions for the exact controllability are revisited for a particular class of degenerate Sobolev systems.

AB - In this paper, we revisit the recently proposed results for a general class of linear stochastic degenerate Sobolev systems with additive noise by using a different approach keeping, however, the main assumptions unchanged for the purpose of comparison. In particular, the mild and strong well-posedness for the initial and final value problems are presented and studied by applying a suitable transformation that formulates the degenerate stochastic system as a pseudoparabolic one. Based on the derived results for the forward and backward cases, under this new framework, the conditions for the exact controllability are revisited for a particular class of degenerate Sobolev systems.

KW - Exact controllability

KW - Singular systems in infinite dimensions

KW - Stochastic backward equations in Hilbert spaces

KW - Stochastic degenerate Sobolev equations

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