Existence and uniqueness of solutions to a flow and transport problem with degenerating coefficients

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics Pub Date : 2022-02-03 DOI:10.1017/s0956792522000018

N. Ray, R. Schulz

引用次数: 1

Abstract

Structural changes of the pore space and clogging phenomena are inherent to many porous media applications. However, related analytical investigations remain challenging due to potentially vanishing coefficients in the respective systems of partial differential equations. In this research, we apply an appropriate scaling of the unknowns and work with porosity-weighted function spaces. This enables us to prove existence, uniqueness and non-negativity of weak solutions to a combined flow and transport problem with vanishing, but prescribed porosity field, permeability and diffusion.

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一类退化系数流与输运问题解的存在唯一性

孔隙空间的结构变化和堵塞现象是许多多孔介质应用所固有的。然而，由于各偏微分方程组中的系数可能会消失，相关的分析研究仍然具有挑战性。在这项研究中，我们应用了未知量的适当比例，并使用孔隙度加权函数空间。这使我们能够证明具有消失但规定的孔隙度场、渗透率和扩散的流动和输运组合问题的弱解的存在性、唯一性和非负性。

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

European Journal of Applied Mathematics 数学-应用数学

CiteScore

4.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.