2016
DOI: 10.1093/imamat/hxw013
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Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

Abstract: We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising 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 this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the ori… Show more

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Cited by 2 publications
(2 citation statements)
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References 17 publications
(26 reference statements)
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“…In [], the authors studied a model of specific structure of a heat and mass transfer arising from textile industry and proved the global existence for one‐dimensional problems in [] and three‐dimensional problems in []. In [], the authors proved the existence of the weak solutions to systems modeling the consolidation of saturated porous media. In [], the author proved the local existence of weak solutions to degenerate quasilinear problems, where the coefficient function in front of the time derivative may vanish at a set of zero measure.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…In [], the authors studied a model of specific structure of a heat and mass transfer arising from textile industry and proved the global existence for one‐dimensional problems in [] and three‐dimensional problems in []. In [], the authors proved the existence of the weak solutions to systems modeling the consolidation of saturated porous media. In [], the author proved the local existence of weak solutions to degenerate quasilinear problems, where the coefficient function in front of the time derivative may vanish at a set of zero measure.…”
Section: Introductionmentioning
confidence: 99%
“…In [28,29,30], the authors studied a model of specific structure of a heat and mass transfer arising from textile industry and proved the global existence for one-dimensional problems in [28,29] and three-dimensional problems in [30]. In [21], the authors proved the existence of the weak solutions to systems modeling the consolidation of saturated porous media.…”
Section: Introductionmentioning
confidence: 99%