Upscaling of a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations originating in the context of crystal dissolution and precipitation inside a porous medium: existence theory and periodic homogenization

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Mahato HS, Kräutle S, Böhm M, Knabner P
Zeitschrift: Advances in Mathematical Sciences and Applications
Jahr der Veröffentlichung: 2017
Band: 26
Heftnummer: 1
Seitenbereich: 39-81
ISSN: 1343-4373


Abstract

In this paper, we consider diffusion and reaction of mobile chemical species,
and dissolution and precipitation of immobile species present inside a porous medium. The
transport of mobile species in the pores is modeled by a system of semilinear parabolic
partial differential equations. The reactions amongst the mobile species are assumed to
be reversible, i.e. both forward and backward reactions are considered. These reversible
reactions lead to highly nonlinear reaction rate terms on the right-hand side of the partial
differential equations. This system of equations for the mobile species is complemented
by flux boundary conditions at the outer boundary. Furthermore, the dissolution and
precipitation of immobile species on the surface of the solid parts are modeled by mass
action kinetics which lead to a nonlinear precipitation term and a multivalued dissolution
term. The model is posed at the pore (micro) scale. The contribution of this paper is two-
fold: first we show the existence of a unique positive global weak solution for the coupled
systems and then we upscale (homogenize) the model from the micro scale to the macro
scale. For the existence of solution, some regularization techniques, Schaefer’s fixed point
theorem and Lyapunov type arguments have been used whereas the concepts of two-scale
convergence and periodic unfolding are used for the homogenization.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Kräutle, Serge PD Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Mahato, Hari Shankar
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Zitierweisen

APA:
Mahato, H.S., Kräutle, S., Böhm, M., & Knabner, P. (2017). Upscaling of a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations originating in the context of crystal dissolution and precipitation inside a porous medium: existence theory and periodic homogenization. Advances in Mathematical Sciences and Applications, 26(1), 39-81.

MLA:
Mahato, Hari Shankar, et al. "Upscaling of a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations originating in the context of crystal dissolution and precipitation inside a porous medium: existence theory and periodic homogenization." Advances in Mathematical Sciences and Applications 26.1 (2017): 39-81.

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