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

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...

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Bibliographic Details
Published inEuropean journal of applied mathematics Vol. 34; no. 1; pp. 55 - 76
Main Authors RAY, NADJA, SCHULZ, RAPHAEL
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.02.2023
Subjects
Applied mathematics
Boundary conditions
Function space
Investigations
Mathematical analysis
Numerical analysis
Oil recovery
Partial differential equations
Permeability
Porosity
Porous media
Uniqueness
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ISSN0956-7925
1469-4425
DOI10.1017/S0956792522000018

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Summary: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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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792522000018