分数阶微分方程的不稳定流形

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Eurasian Journal of Mathematical and Computer Applications 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。

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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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来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.