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Ill-Posed Hele—Shaw Flows

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Free Boundary Problems

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 147))

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Abstract

The Hele—Shaw flow, introduced at the end of the 19th Century in [14], is a model approximation of the motion of two immiscible fluids confined between two parallel planes, separated by a small distance 0 < h « L, where L is a characteristic transversal length. Such a device is called a Hele—Shaw Cell. Its physical interest rests on its formal analogy with Darcy’s law. This makes it suitable for designing simulations of the flow of immiscible fluids in a porous medium.

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Author information

Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici, Università di Roma La Sapienza, Via A. Scarpa 16, Rome, 00161, Italy

    Daniele Andreucci

  2. ITC-CNR, Via C. Marx 43, Rome, Italy

    Giovanni Caruso

  3. Dept. of Mathematics, Stevenson Center, Vanderbilt University, Nashville, TN, 37240, USA

    Emmanuele DiBenedetto

Authors
  1. Daniele Andreucci
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  2. Giovanni Caruso
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  3. Emmanuele DiBenedetto
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, Pavia, 27100, Italy

    Pierluigi Colli

  2. Dipartimento di Matematica, Università di Milano, Via Saldini, 50, Milano, 20133, Italy

    Claudio Verdi

  3. Dipartimento di Matematica, Via Sommarive, 14, Povo di Trento, 38050, Italy

    Augusto Visintin

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© 2003 Springer Basel AG

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Andreucci, D., Caruso, G., DiBenedetto, E. (2003). Ill-Posed Hele—Shaw Flows. In: Colli, P., Verdi, C., Visintin, A. (eds) Free Boundary Problems. ISNM International Series of Numerical Mathematics, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7893-7_3

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  • DOI: https://doi.org/10.1007/978-3-0348-7893-7_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9613-9

  • Online ISBN: 978-3-0348-7893-7

  • eBook Packages: Springer Book Archive

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