Solvability Analysis for a Class of Mixed Variational-Hemivariational Inequalities

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-10-07 Epub Date: 2026-08-10 DOI:10.1002/mma.70936

Min Zhou, Xin Tan, Jianwei Hao

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引用次数: 0

Abstract

This article investigates the existence and uniqueness of solutions to mixed variational-hemivariational inequalities. Unlike existing approaches in published literature on mixed variational-hemivariational inequalities, our method for analyzing existence and uniqueness is easy to understand and apply. Moreover, a projection iterative algorithm is provided for solving such inequalities. First, the existence of a solution for an auxiliary hemivariational problem is established. Subsequently, two sequences corresponding to the problem variables are constructed via projection operators. By leveraging the projection theorem and operator properties, the convergence of both sequences is rigorously demonstrated, thereby proving that the limit of the sequences constitutes the unique solution to the mixed variational-hemivariational inequality. Finally, we provide examples such that $X, Y, 𝒳, Λ, γ, T, A, b, φ, ψ, J$ satisfy the working hypotheses to illustrate the theory.

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一类混合变分-半变分不等式的可解性分析

本文研究了一类混合变分-半变分不等式解的存在唯一性。与已有的关于混合变分-半变分不等式的方法不同，我们的存在唯一性分析方法易于理解和应用。并给出了求解此类不等式的投影迭代算法。首先，建立了一类辅助半变分问题解的存在性。然后，通过投影算子构造了两个与问题变量对应的序列。利用投影定理和算子性质，严格证明了这两个序列的收敛性，从而证明了这两个序列的极限构成了变分-半变分混合不等式的唯一解。最后，我们给出了这样的例子：X， Y, f， Λ， γ， T， A，b, φ, ψ， J满足说明理论的工作假设。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.