Geodesic
On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis
Piotr Biler 1   ; Lorenzo Brandolese 2
1 Instytut Matematyczny Uniwersytet Wroc/lawski pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2 Université de Lyon Université Lyon 1 Institut Camille Jordan, CNRS UMR 5208 43 bd. du 11 Novembre 69622 Villeurbanne Cedex, France
Studia Mathematica, Tome 193 (2009) no. 3, pp. 241-261 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller–Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
DOI : 10.4064/sm193-3-2
Keywords: establish results convergence strong topologies solutions parabolic parabolic keller segel system plane corresponding solutions parabolic elliptic model physical parameter goes zero main tools suitable space time estimates implying global existence slowly decaying general nonintegrable solutions these models under natural smallness assumption

Piotr Biler  1   ; Lorenzo Brandolese  2

1 Instytut Matematyczny Uniwersytet Wroc/lawski pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2 Université de Lyon Université Lyon 1 Institut Camille Jordan, CNRS UMR 5208 43 bd. du 11 Novembre 69622 Villeurbanne Cedex, France 
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     title = {On the parabolic-elliptic limit of the doubly parabolic
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Piotr Biler; Lorenzo Brandolese. On the parabolic-elliptic limit of the doubly parabolic
 Keller–Segel system modelling chemotaxis. Studia Mathematica, Tome 193 (2009) no. 3, pp. 241-261. doi: 10.4064/sm193-3-2

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