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arXiv · 1508.03550

Forward-Backward Evolution Equations and Applications

Jiongmin Yong
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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.

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Jiongmin Yong. 2015-08-14. Forward-Backward Evolution Equations and Applications. https://arxiv.org/abs/1508.03550

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