Weak and Classical Solutions to Multispecies Advection–Dispersion Equations in Multilayer Porous Media

Miglena N. Koleva () and Lubin G. Vulkov ()
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Miglena N. Koleva: Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria
Lubin G. Vulkov: Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria

Mathematics, 2023, vol. 11, issue 14, 1-18

Abstract: The basic model motivating this work is that of contaminant transport in the Earth’s subsurface, which contains layers in which analytical and semi-analytical solutions of the corresponding advection–dispersion equations could be derived. Then, using the interface relations between adjacent layers, one can streamline the study of the model to the solution to the initial boundary value problem for a coupled parabolic system on partitioned domains. For IBVPs, we set up weak formulations and prove the existence and uniqueness of solutions to appropriate Sobolev-like spaces. A priori estimates at different levels of input data smoothness were obtained. The nonnegativity preservation over time of the solution is discussed. We numerically demonstrate how to solve the reduced truncated problem instead of the original multispecies one with a large number of layers.

Keywords: interface-coupled multispecies problem; reduced truncated problem; Sobolev spaces; positivity preservation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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