Forward-Backward Evolution Equations And Applications

Keywords

Decoupling field; Forward-backward evolution equations; Lyapunove operator; Method of continuation

Abstract

Well-posedness is studied for a special system of two-point boundary value problem for evolution equations which is called a forward-backward evolution equation (FBEE, for short). Two approaches are introduced: A decoupling method with some brief discussions, and a method of continuation with some substantial discussions. For the latter, we have introduced Lyapunov operators for FBEEs, whose existence leads to some uniform a priori estimates for the mild solutions of FBEEs, which will be sufficient for the wellposedness. For some special cases, Lyapunov operators are constructed. Also, from some given Lyapunov operators, the corresponding solvable FBEEs are identified.

Publication Date

12-1-2016

Publication Title

Mathematical Control and Related Fields

Volume

6

Issue

4

Number of Pages

653-704

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3934/mcrf.2016019

Socpus ID

84991467154 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84991467154

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