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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 4, 2000, pp. 977–997
DOI: 10.4171/ZAA/993

Published online: 2000-12-31

Hysteresis in Filtration through Porous Media

F. Bagagiolo[1] and Augusto Visintin[2]

(1) Università di Padova, Italy
(2) Università di Trento, Italy

We study an evolution problem for filtration through porous media, accounting for hysteresis in the saturation versus pressure constitutive relation. We provide a weak formulation of the problem, assuming that the memory effect in the constitutive relation consists not only of a rate-independent component but also of a rate-dependent one. We prove an existence result, which also applies to the case where the hysteresis operator is of Preisach-type.

Keywords: Degenerate parabolic equations, hysteresis, filtration, variational inequalities

Bagagiolo F., Visintin Augusto: Hysteresis in Filtration through Porous Media. Z. Anal. Anwend. 19 (2000), 977-997. doi: 10.4171/ZAA/993