A class of nonlocal parabolic problems occurring in statistical mechanics
Volume 66 / 1993
Colloquium Mathematicum 66 (1993), 131-145
DOI: 10.4064/cm-66-1-131-145
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.
