Well-posedness results and global attractors for a generalized coupled dynamical system

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2026-12-01 Epub Date: 2026-02-04 DOI:10.1016/j.nonrwa.2026.104615

Xiuwen Li , Zhenhai Liu , Jing Zhao

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引用次数: 0

Abstract

Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (m-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.

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一类广义耦合动力系统的适定性结果和全局吸引子

本文研究了一类新的广义耦合动力系统的适定性和全局吸引子的理论结果。该系统由一个具有历史相关算子的抽象非线性微分包含和一个具有两个历史相关算子的广义变分-半变分不等式（GVHVI）组成，在Banach空间中表述。我们的研究从四个关键方面展开。首先，利用多值映射的满射定理和非线性泛函分析技术，引入并建立了GVHVI的适定性结果。其次，在适当的假设条件下，利用不动点理论，考虑并讨论了gcds解的存在性。第三，在一些充分条件下，我们探索并推导了由gcds描述的多值半流（m-半流）的全局吸引子的存在性。最后，我们给出了一个耦合问题的应用，证明了我们的理论发现的适用性。

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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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.