# Equilibration of aggregation-diffusion equations with weak interaction forces.

@article{Shu2020EquilibrationOA, title={Equilibration of aggregation-diffusion equations with weak interaction forces.}, author={Ruiwen Shu}, journal={arXiv: Analysis of PDEs}, year={2020} }

This paper studies the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the unique steady state as time goes to infinity (equilibration), with an explicit algebraic rate. The proof is based on a uniform-in-time bound on the first moment of the density distribution, combined with an energy dissipation rate estimate. This is the first… CONTINUE READING

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