\网络上一些半线性边界方程的伪近周期解

IF 0.9 Q2 MATHEMATICS
Thami Akrid, Mahmoud Baroun
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引用次数: 0

摘要

本研究涉及在顶点非均质条件下有限网络边缘某些传输过程的()伪近周期解的存在性和唯一性。为此,我们的策略是把这些系统看作半线性边界演化方程的一个特殊案例。\displaystyle {\frac{du}{dt}} &{}= A_{m} u(t)+f(t,u(t)),\quad t\in {\mathbb {R}}, \ L u(t)&{} = g(t,u(t)) ,\quad t\in {\mathbb {R}},\\\end{array}\right.}\end{aligned}$$where \(A:= A_m|ker L\) generates a C\(_0\)-semigroup admitting an exponential dichotomy on a Banach space.假设分别在状态空间和边界空间取值的强制项只是斯捷潘诺夫意义上的\(\mu \)-伪近周期,我们证明(SHBE)有一个唯一的\(\mu \)-伪近周期解,它满足常数的变化式。然后,我们将前面的结果应用到我们的网络模型中,得到了 \(\mu \)-伪几乎周期解的存在性和唯一性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
\(\mu \)-Pseudo almost periodic solutions to some semilinear boundary equations on networks

This work deals with the existence and uniqueness of \(\mu \)-pseudo almost periodic solutions to some transport processes along the edges of a finite network with inhomogeneous conditions in the vertices. For that, the strategy consists of seeing these systems as a particular case of the semilinear boundary evolution equations

$$\begin{aligned} (SHBE)\;{\left\{ \begin{array}{ll} \displaystyle {\frac{du}{dt}} &{}= A_{m} u(t)+f(t,u(t)),\quad t\in {\mathbb {R}}, \\ L u(t)&{} = g(t,u(t)) ,\quad t \in {\mathbb {R}},\\ \end{array}\right. } \end{aligned}$$

where \(A:= A_m|ker L\) generates a C\(_0\)-semigroup admitting an exponential dichotomy on a Banach space. Assuming that the forcing terms taking values in a state space and in a boundary space respectively are only \(\mu \)-pseudo almost periodic in the sense of Stepanov, we show that (SHBE) has a unique \(\mu \)-pseudo almost periodic solution which satisfies a variation of constant formula. Then we apply the previous result to obtain the existence and uniqueness of \(\mu \)-pseudo almost periodic solution to our model of network.

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来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
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