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Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media
Università di Roma La Sapienza.
Università di Roma La Sapienza.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Eindhoven University of Technology. (Mathematics)ORCID iD: 0000-0002-1160-0007
2017 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 82, no 1, 224-250 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Oxford University Press, 2017. Vol. 82, no 1, 224-250 p.
Keyword [en]
weak solutions; cross-diffusion system; energy method; Leray–Schauder fixed-point theorem; finite differences; consolidation of porous media
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-40730DOI: 10.1093/imamat/hxw013ISI: 000393103500009OAI: oai:DiVA.org:kau-40730DiVA: diva2:907309
Available from: 2016-02-26 Created: 2016-02-26 Last updated: 2017-07-06Bibliographically approved

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