Abstract:
This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by no way an exhaustive review of the methods and results involving the entropy, not even in the field of PDEs. Many other researchers in and outside Europe have contributed to the development of this field, including - but not only - in collaboration with some of the people of the group. However, it can be claimed that this group had a leading role over the recent years and this essay is intended to explain how this occurred.
Registro:
Documento: |
Artículo
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Título: | Entropies and equilibria of many-particle systems: An essay on recent research |
Autor: | Arnold, A.; Carrillo, J.A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P.A.; Toscani, G.; Villani, C. |
Filiación: | Universität Münster, Germany Univ. Autónoma de Barcelona, Spain Ecl. Normale Sup. de Cachan, France Université Paris IX Dauphine, France Universität Mainz, Germany Universidad de Buenos Aires, Argentina University of Vienna, Australia University of Pavia, Italy Ecl. Normale Sup. de Lyon, France Inst. für Numerische Mathematik, Universität Münster, D-48149 Münster, Germany ICREA, Departamento de Matemática, Univ. Autónoma de Barcelona, 08193-Bellaterra, Spain Ecl. Normale Sup. de Cachan, 61, avenue du President Wilson, 94235 Cachan, France Ceremade, Université Paris IX Dauphine, Place de Lattre de Tassigny, F-75775 Paris, France Fb. Mathematik und Informatik, Universität Mainz, Germany Departamento de Matemática, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Faculty of Mathematics, Nordbergstrasse 15, Vienna, Austria Department of Mathematics, University of Pavia, via Ferrata 1, 27100 Pavia, Italy Ecl. Normale Sup. de Lyon, 46 Allée d'Italie, F-69364 Lyon, France
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Palabras clave: | Entropy; Entropy production; Large-time behavior |
Año: | 2004
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Volumen: | 142
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Número: | 1-2
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Página de inicio: | 35
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Página de fin: | 43
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DOI: |
http://dx.doi.org/10.1007/s00605-004-0239-2 |
Título revista: | Monatshefte fur Mathematik
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Título revista abreviado: | Monatsh. Math.
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ISSN: | 00269255
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00269255_v142_n1-2_p35_Arnold |
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Citas:
---------- APA ----------
Arnold, A., Carrillo, J.A., Desvillettes, L., Dolbeault, J., Jüngel, A., Lederman, C., Markowich, P.A.,..., Villani, C.
(2004)
. Entropies and equilibria of many-particle systems: An essay on recent research. Monatshefte fur Mathematik, 142(1-2), 35-43.
http://dx.doi.org/10.1007/s00605-004-0239-2---------- CHICAGO ----------
Arnold, A., Carrillo, J.A., Desvillettes, L., Dolbeault, J., Jüngel, A., Lederman, C., et al.
"Entropies and equilibria of many-particle systems: An essay on recent research"
. Monatshefte fur Mathematik 142, no. 1-2
(2004) : 35-43.
http://dx.doi.org/10.1007/s00605-004-0239-2---------- MLA ----------
Arnold, A., Carrillo, J.A., Desvillettes, L., Dolbeault, J., Jüngel, A., Lederman, C., et al.
"Entropies and equilibria of many-particle systems: An essay on recent research"
. Monatshefte fur Mathematik, vol. 142, no. 1-2, 2004, pp. 35-43.
http://dx.doi.org/10.1007/s00605-004-0239-2---------- VANCOUVER ----------
Arnold, A., Carrillo, J.A., Desvillettes, L., Dolbeault, J., Jüngel, A., Lederman, C., et al. Entropies and equilibria of many-particle systems: An essay on recent research. Monatsh. Math. 2004;142(1-2):35-43.
http://dx.doi.org/10.1007/s00605-004-0239-2