一类新的偏微分拟变分和抛物型变分不等式系统解的存在性及其应用

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1837-1856.

一类新的偏微分拟变分和抛物型变分不等式系统解的存在性及其应用

李为¹^,², 唐正辉¹^,³, 吴增宝⁴^,^*(), 杨春艳⁵, 蔡昊煜¹

¹ 成都理工大学数学科学学院成都 610059
² 成都理工大学数学研究中心成都 610059
³ 成都理工大学数学地质四川省重点实验室成都 610059
⁴ 洛阳师范学院数学科学学院河南洛阳 471934
⁵ 四川大学数学学院成都 610059

收稿日期:2025-11-30 修回日期:2026-04-27 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 吴增宝 E-mail:zengbaowu@hotmail.com
基金资助:
国家自然科学基金(12301395);国家自然科学基金(11901273);河南省高校科技创新人才计划(23HASTIT031);河南省自然科学基金(252300421997)

A New Partial Differential Nonlinear System Containing Quasivariational and Parabolic Variational Inequalities and Its Application

Wei Li¹^,², Zhenghui Tang¹^,³, Zengbao Wu⁴^,^*(), Chunyan Yang⁵, Haoyu Cai¹

¹ School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059
² Mathematics Research Center, Chengdu University of Technology, Chengdu 610059
³ Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059
⁴ Department of Mathematics, Luoyang Normal University, Henan Luoyang 471934
⁵ Department of Mathematics, Sichuan University, Chengdu 610064

Received:2025-11-30 Revised:2026-04-27 Online:2026-10-26 Published:2026-09-07
Contact: Zengbao Wu E-mail:zengbaowu@hotmail.com
Supported by:
NSFC(12301395);NSFC(11901273);Program for Science and Technology Innovation Talents in Universities of Henan Province(23HASTIT031);Natural Science Foundation of Henan(252300421997)

摘要/Abstract

摘要：

该文在 Hilbert 空间上研究由偏微分方程、拟变分不等式与抛物型变分不等式耦合而成的一类新的非线性耦合系统. 利用 Banach 不动点定理, 在合适的假设条件下, 证明了该耦合系统解的存在唯一性, 并将所得理论结果应用于求解具有长记忆效应、磨损演化与损伤效应的粘弹性摩擦接触问题.

关键词: 偏微分变分不等式, 拟变分不等式, 抛物型变分不等式, 粘弹性摩擦接触问题

Abstract:

This paper investigates a new class of nonlinear coupled systems on Hilbert spaces, consisting of partial differential equations, quasi-variational inequalities, and parabolic variational inequalities. Using the Banach fixed-point theorem, we prove the existence and uniqueness of solutions for this coupled system under appropriate assumptions, and apply the resulting theoretical findings to solve viscoelastic friction contact problems involving long-memory effects, wear evolution, and damage effects.

Key words: partial differential variational inequality, quasivariational inequality, parabolic variational inequality, viscoelastic friction contact problems

中图分类号:

O177.91

李为, 唐正辉, 吴增宝, 杨春艳, 蔡昊煜. 一类新的偏微分拟变分和抛物型变分不等式系统解的存在性及其应用[J]. 数学物理学报, 2026, 46(5): 1837-1856.

Wei Li, Zhenghui Tang, Zengbao Wu, Chunyan Yang, Haoyu Cai. A New Partial Differential Nonlinear System Containing Quasivariational and Parabolic Variational Inequalities and Its Application[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1837-1856.

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