演化方程控制的双曲型Clarke次微分内含体的双步Rothe格式

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-07-24 DOI:10.1016/j.nonrwa.2025.104463

Jinxia Cen , Krzysztof Bartosz , Jen-Chih Yao , Shengda Zeng

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引用次数: 0

摘要

本文研究了Banach空间中由双曲型Clarke次微分包含和演化方程组成的耦合系统。利用基于双步格式的时间半离散方法，构造了一个离散近似系统。利用多值伪单调算子的满射性和离散Gronwall不等式，给出了离散近似系统解的存在性及其先验估计。最后，我们证明了离散近似系统的解序列弱收敛于一个极限单元，该极限单元是耦合原始系统的解。

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A double step Rothe scheme for hyperbolic Clarke subdifferential inclusions controlled by evolution equations

In this paper we deal with a coupled system which consists of a hyperbolic Clarke subdifferential inclusion and an evolution equation in Banach spaces. Using temporally semidiscrete method based on the double step scheme, we construct a discrete approximate system. The existence of solutions and its a-priori estimates for the discrete approximate system are provided by the surjectivity of multivalued pesudomonotone operators and discrete Gronwall’s inequality. Finally, we show that the solution sequence of the discrete approximate system converges weakly to a limit element, which is a solution of the coupled original system.

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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.