Stochastic degenerate Sobolev equations: well posedness and exact controllability

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

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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 languageEnglish
Pages (from-to)1025-1032
Number of pages8
JournalMathematical Methods in the Applied Sciences
Volume41
Issue number3
DOIs
Publication statusPublished - 1 Feb 2018
Externally publishedYes

Keywords

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

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