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Weak solutions to A...
Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media
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- Artale Harris, Pietro (author)
- Università di Roma La Sapienza
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- Cirillo, Emilio N.M (author)
- Università di Roma La Sapienza
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- Muntean, Adrian, 1974- (author)
- Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013),Eindhoven University of Technology,Mathematics
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(creator_code:org_t)
- 2016-04-12
- 2017
- English.
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In: IMA Journal of Applied Mathematics. - : Oxford University Press. - 0272-4960 .- 1464-3634. ; 82:1, s. 224-250
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Abstract
Subject headings
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- We study the weak solvability of a system of coupled Allen–Cahn-like equations resembling cross-diffusion which arises as a model for the consolidation of saturated porous media. Besides using energy-like estimates, we cast the special structure of the system in the framework of the Leray–Schauder fixed-point principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- weak solutions; cross-diffusion system; energy method; Leray–Schauder fixed-point theorem; finite differences; consolidation of porous media
- Matematik
- Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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