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Title

A class of nonlocal parabolic problems occurring in statistical mechanics

Authors 1, 1

Affiliations

  1. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.

Keywords

ENG
nonlinear boundary conditions, stationary solutions, existence of solutions, parabolic-elliptic system

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Colloquium Mathematicum
1993/66/1
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Pages:
131-145
Main language of publication
English
Received
1993-03-15
Published
1993
Exact and natural sciences