On stationary and radially symmetric solutions to some drift–diffusion equations with nonlocal term

Abstract

In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some drift–diffusion equation modelling among others systems of self-gravitating particles in astrophysics when one looks for its stationary solutions. The model is also related to chemotaxis phenomenon in microbiology and in two dimensional stationary case it appears in the context of hydrodynamics describing 2-D vortices.

Keywords:

• drift–diffusion
• nonlocal elliptic equation
• Fermi–Dirac statistics

AMS Subject Classifications:

• 35Q85
• 47H10
• 85A05

Notes

This work is partially supported by the Polish Ministry of Science and Higher Education project N N201 418839.