无限延迟演化方程的可容许惯性流形

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2021-01-01 DOI:10.4134/BKMS.B200462

Le Anh Minh

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引用次数: 1

摘要

本文的目的是为了证明一个容许惯性流形的存在轻微解决无限延迟演化方程的形式du / dt +非盟= F (t, ut), t≥年代,我们(θ)=φ(θ),∀θ∈(−∞,0),s∈R,在正定,自伴的离散谱,李普希茨系数的非线性F可能取决于时间和属于一部分容许函数空间上定义整个线。该证明基于李雅普诺夫-佩龙方程，并结合可容许性和对偶性估计。

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ADMISSIBLE INERTIAL MANIFOLDS FOR INFINITE DELAY EVOLUTION EQUATIONS

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form  du dt +Au = F (t, ut), t ≥ s, us(θ) = φ(θ), ∀θ ∈ (−∞, 0], s ∈ R, where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).