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Nonlinear mean-field Fokker-Planck equations and their applications in physics, astrophysics and biology

Pierre-Henri Chavanis
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Abstract

We discuss a general class of nonlinear mean-field Fokker-Planck equations [P.H. Chavanis, Phys. Rev. E, 68, 036108 (2003)] and show their applications in different domains of physics, astrophysics and biology. These equations are associated with generalized entropic functionals and non-Boltzmannian distributions (Fermi-Dirac, Bose-Einstein, Tsallis,...). They furthermore involve an arbitrary binary potential of interaction. We emphasize analogies between different topics (two-dimensional turbulence, self-gravitating systems, Debye-Hückel theory of electrolytes, porous media, chemotaxis of bacterial populations, Bose-Einstein condensation, BMF model, Cahn-Hilliard equations,...) which were previously disconnected. All these examples (and probably many others) are particular cases of this general class of nonlinear mean-field Fokker-Planck equations.

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BibTeXRIS

Pierre-Henri Chavanis. 2006-11-03. Nonlinear mean-field Fokker-Planck equations and their applications in physics, astrophysics and biology. https://doi.org/10.1016/j.crhy.2006.01.004

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