A kinetic approximation of Hele–Shaw flow

Lorenzo Pareschi; Giovanni Russo; Giuseppe Toscani

doi:10.1016/j.crma.2003.11.006

Mathematical Problems in Mechanics

A kinetic approximation of Hele–Shaw flow

Presented by: Carlo Cercignani

Lorenzo Pareschi ¹; Giovanni Russo ²; Giuseppe Toscani ³

¹ Department of Mathematics, University of Ferrara, via Machiavelli 35, 35100 Ferrara, Italy
² Department of Mathematics and Computer Science, University of Catania, viale Andrea Doria 6, 95125 Catania, Italy
³ Department of Mathematics, University of Pavia, via Ferrata 1, 27100 Pavia, Italy

Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 177-182.

Abstract
Résumé

In this Note we consider a fourth order degenerate parabolic equation modeling the evolution of the interface of a spreading droplet. The equation is approximated trough a collisional kinetic equation. This permits to derive numerical approximations that preserves positivity of the solution and the main relevant physical properties. A Monte Carlo application is also shown.

Dans cette Note, nous considérons une équation dégénérée du quatrième ordre modélisant l'évolution de l'interface d'une goutte. L'équation est approchée par une équation collisionnelle cinétique. Cela permet de construire des approximations numériques qui préservent la positivité de la solution et ses principales propriétés physiques. Un exemple « Monte-Carlo » est aussi présenté.

Received: 2003-06-26
Accepted: 2003-11-04
Published online: 2003-12-11

DOI: 10.1016/j.crma.2003.11.006

Author's affiliations:

Lorenzo Pareschi ¹; Giovanni Russo ²; Giuseppe Toscani ³

¹ Department of Mathematics, University of Ferrara, via Machiavelli 35, 35100 Ferrara, Italy
² Department of Mathematics and Computer Science, University of Catania, viale Andrea Doria 6, 95125 Catania, Italy
³ Department of Mathematics, University of Pavia, via Ferrata 1, 27100 Pavia, Italy

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     author = {Lorenzo Pareschi and Giovanni Russo and Giuseppe Toscani},
     title = {A kinetic approximation of {Hele{\textendash}Shaw} flow},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {177--182},
     publisher = {Elsevier},
     volume = {338},
     number = {2},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.006},
     language = {en},
}

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Lorenzo Pareschi; Giovanni Russo; Giuseppe Toscani. A kinetic approximation of Hele–Shaw flow. Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 177-182. doi : 10.1016/j.crma.2003.11.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.006/

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