为动脉支架血管内药物释放和动脉组织内运输建模的 PDE 系统进行数学和数值分析

IF 2.6 4区工程技术 Q1 Mathematics

Mathematical Biosciences and Engineering Pub Date : 2024-04-21 DOI:10.3934/mbe.2024248

Xiaobing Feng, Tingao Jiang

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引用次数: 0

摘要

本文涉及改进的一维血管内支架模型的 PDE（偏微分方程）和数值分析。通过使用 Galerkin 方法并结合紧凑性论证，证明了修改后的模型具有唯一的弱解。针对 PDE 模型制定了半离散有限元法和使用欧拉时间步进的全离散方案。两种方案都证明了能量规范中的最优阶误差估计。此外，还给出了数值结果，并对不同的解耦策略和时间步进方案进行了比较。最后，还简要讨论了该模型及其 PDE 和数值分析结果在二维情况下的扩展。

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Mathematical and numerical analysis for PDE systems modeling intravascular drug release from arterial stents and transport in arterial tissue

This paper is concerned with the PDE (partial differential equation) and numerical analysis of a modified one-dimensional intravascular stent model. It is proved that the modified model has a unique weak solution by using the Galerkin method combined with a compactness argument. A semi-discrete finite-element method and a fully discrete scheme using the Euler time-stepping have been formulated for the PDE model. Optimal order error estimates in the energy norm are proved for both schemes. Numerical results are presented, along with comparisons between different decoupling strategies and time-stepping schemes. Lastly, extensions of the model and its PDE and numerical analysis results to the two-dimensional case are also briefly discussed.

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来源期刊

Mathematical Biosciences and Engineering 工程技术-数学跨学科应用

CiteScore

3.90

自引率

7.70%

发文量

586

审稿时长

>12 weeks

期刊介绍： Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).