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Miguel Escobedo (2002)
RACSAM
We first present very elementary relations between climate and aerosols. The we introduce the homogeneous coagulation equation as a simple model to describe systems of merging particles like polymers or aerosols. We next give a recent result about gelation of solutions. We end with some related open questions.
Yuri Kondratiev, Eugene Lytvynov (2005)
Annales de l'I.H.P. Probabilités et statistiques
Piotr Biler, Lorenzo Brandolese (2006)
Colloquium Mathematicae
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.
Carole Rosier, Lionel Rosier (2004)
Banach Center Publications
Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.
Piotr Biler (1995)
Applicationes Mathematicae
We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.
Piotr Biler, Tadeusz Nadzieja (1995)
Applicationes Mathematicae
Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.
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