Self-interaction of Brownian particles coupled with thermodynamic processes. (English) Zbl 1010.82028
Summary: We propose some nonlinear parabolic-elliptic systems modelling the evolution of the density of particles (charged or massive) interacting with themselves, and coupled to a temperature field. These models are thermodynamically consistent, i.e., they obey the first and the second laws of thermodynamics. We study their steady states and the asymptotic behaviour for large time.
MSC:
| 82C35 | Irreversible thermodynamics, including Onsager-Machlup theory |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
Keywords:
nonequilibrium thermodynamics; interaction of particles; nonlinear parabolic-elliptic systemsReferences:
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