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 | |
| 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
Cite this
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Stochastic degenerate Sobolev equations : well posedness and exact controllability. / Liaskos, Konstantinos B.; Stratis, Ioannis G.; Pantelous, Athanasios A.
In: Mathematical Methods in the Applied Sciences, Vol. 41, No. 3, 01.02.2018, p. 1025-1032.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Stochastic degenerate Sobolev equations
T2 - well posedness and exact controllability
AU - Liaskos, Konstantinos B.
AU - Stratis, Ioannis G.
AU - Pantelous, Athanasios A.
PY - 2018/2/1
Y1 - 2018/2/1
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
UR - http://www.scopus.com/inward/record.url?scp=84994152044&partnerID=8YFLogxK
U2 - 10.1002/mma.4077
DO - 10.1002/mma.4077
M3 - Article
VL - 41
SP - 1025
EP - 1032
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 3
ER -