分数阶微分方程的不稳定流形

Pub Date : 2022-09-27 DOI:10.32523/2306-6172-2022-10-3-58-72

Piskarev Sergey, Siegmund Stefan

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引用次数: 0

摘要

在Banach空间上，我们证明了一个抽象的半线性分数阶微分方程Dαu（t）=Au（t）+f（t），u（0）=u0的不稳定流形的存在性。然后，我们发展了一种通用的方法来建立不稳定流形的半离散逼近。我们的结果的主要假设自然是令人满意的。特别是，这对于具有紧致预解式的算子是正确的，并且可以对有限元和有限差分方法进行验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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UNSTABLE MANIFOLDS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

We prove the existence of unstable manifolds for an abstract semilinear fractional differential equation Dαu(t) = Au(t) + f(u(t)), u(0) = u 0 , on a Banach space. We then develop a general approach to establish a semidiscrete approximation of unstable manifolds. The main assumption of our results are naturally satisfied. In particular, this is true for operators with compact resolvents and can be verified for finite elements as well as finite differences methods.

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