Forward-Backward Evolution Equations and Applications
Probability
2015-08-17 v1
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 well-posedness. For some special cases, Lyapunov operators are constructed. Also, from some given Lyapunov operators, the corresponding solvable FBEEs are identified.
Cite
@article{arxiv.1508.03550,
title = {Forward-Backward Evolution Equations and Applications},
author = {Jiongmin Yong},
journal= {arXiv preprint arXiv:1508.03550},
year = {2015}
}
Comments
52 pages