Asymptotic behaviour of some nonlocal diffusion problems

Abstract

We deal with a parabolic equation having a diffusion coefficient depending on a nonlocal quantity. We investigate the convergence of the solution towards a steady state, extending previous results obtained by [M. Chipot and B. Lovat (1999). On the asympotic behaviour of some nonlocal problems. Positivity, 3, 65-81]. Using the dynamical systems point of view, we are able to treat the case of a continuum of steady states

Keywords:

• Nonlocal diffusion.
• Asymptotic behaviour
• Steady States:a)limit set

AMS Classification:

• 35K55
• 35B40

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.

Additional information

Notes on contributors

Chipot Michel