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Forward-backward evolution equations and applications
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2016-10-01 , DOI: 10.3934/mcrf.2016019
Jiongmin Yong

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.

中文翻译:

前向后向演化方程及应用

适定性研究了一种特殊的演化方程的两点边值问题系统,称为前向-后向演化方程(简称FBEE)。介绍了两种方法:一种带有一些简短讨论的解耦方法,以及一种带有一些实质性讨论的继续方法。对于后者,我们为 FBEE 引入了 Lyapunov 算子,它的存在导致了对 FBEE 的温和解的一些统一的先验估计,这对于适定性来说是足够的。对于一些特殊情况,构造了李雅普诺夫算子。此外,从一些给定的 Lyapunov 算子中,确定了相应的可解 FBEE。
更新日期:2016-10-01
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