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A hysteresis model for fluid diffusion in a deformable porous medium

Prof. Pavel Krejci(Institute of Mathematics, Czech Academy of Sciences, Prague)
Friday, April 12th, 2019, 2:40 PM  闵行数学楼102报告厅
Pavel Krejci博士,捷克著名数学家,捷克科学院数学研究所研究员,原所长(2009-2014)。研究工作涉及数学、力学、金融等多个领域,曾在美国University of Wisconsin、法国Universite de Technologie de Compiegne、意大利Universita di Pavia、德国Weierstrass Institute (WIAS)、Universitat Kaiserslautern等科研院所工作。在国际著名杂志发表学术论文139篇,出版专著2部,多次受邀在一些重要的国际会议上做大会邀请报告。获得捷克科学研究奖(2001年)、Bolzano数学奖(Bernard Bolzano Honorary Medal for Merit in Mathematical Sciences)等奖项。

In a deformable porous solid filled with two immiscible fluids (water and air, say), two sources of hysteresis are observed: the solid itself is subject to irreversible plastic deformations, and the fluid flow exhibits capillary hysteresis which can be explained by the surface tension on the interfaces between the two fluids. We propose a model for all these phenomena in the form of a PDE system with hysteresis operators. It is derived from general thermodynamic principles under the hypothesis that the fluid diffusion is slow and the deformations are small. The unknowns of the problem are the capillary pressure, the displacement in the solid, and the absolute temperature. The model can be extended by the possibility of phase transitions (freezing and melting) of the liquid with different specific volumes of the liquid and solid phases. This a joint work with Bettina Detmann, Elisabetta Rocca, and Juergen Sprekels.

主持人:张艳艳 副教授
主办单位:数学科学学院 科技处
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