Geodesic
Global existence versus blow up for some models of interacting particles
Piotr Biler 1   ; Lorenzo Brandolese 2
1 Instytut Matematyczny Uniwersytet Wroc/lawski Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2 Institut Camille Jordan Université Claude Bernard-Lyon 1 21 avenue Claude Bernard 69622 Villeurbanne Cedex, France
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 293-303 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
DOI : 10.4064/cm106-2-9
Keywords: study global existence space time asymptotics solutions class nonlocal parabolic semilinear equations models include nernst planck debye ckel drift diffusion systems parabolic elliptic systems chemotaxis model self gravitating particles result finite time blow solutions localized oscillating complex valued initial using method due montgomery smith

Piotr Biler  1   ; Lorenzo Brandolese  2

1 Instytut Matematyczny Uniwersytet Wroc/lawski Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2 Institut Camille Jordan Université Claude Bernard-Lyon 1 21 avenue Claude Bernard 69622 Villeurbanne Cedex, France 
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Piotr Biler; Lorenzo Brandolese. Global existence versus blow up
 for some models of interacting particles. Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 293-303. doi: 10.4064/cm106-2-9

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