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Stochastic degenerate Sobolev equations: well posedness and exact controllability
Author(s) -
Liaskos Konstantinos B.,
Stratis Ioannis G.,
Pantelous Athanasios A.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4077
Subject(s) - controllability , degenerate energy levels , mathematics , sobolev space , class (philosophy) , transformation (genetics) , initial value problem , mathematical analysis , pure mathematics , computer science , physics , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene
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. Copyright © 2016 John Wiley & Sons, Ltd.