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Global existence versus blow up for some models of interacting particles

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Biler P., Brandolese L.

Colloquium Mathematicum

2006

tom 106

nr 2

293-303

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.

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

100%

Biler P., Brandolese L.

Studia Mathematica

2009

tom 193

nr 3

241-261

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Biler P.

2 Brandolese L.

1 2009

1 2006

Wyniki wyszukiwania

Global existence versus blow up for some models of interacting particles

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis