期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 15, 期 4, 页码 2213-2226出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1069006
关键词
metastability; aggregation model; steady states; diffusion; asymptotic analysis
资金
- AARMS postdoctoral fellowship
- NSERC discovery
- NSERC accelerator grants
We study the long-time effect of noise on pattern formation for the aggregation model. We consider aggregation kernels that generate patterns consisting of two delta-concentrations. Without noise, there is a one-parameter family of admissible equilibria that consist of two concentrations whose mass is not necessary equal. We show that when a small amount of noise is added, the heavier concentration leaks its mass towards the lighter concentration over a very long time scale, eventually resulting in the equilibration of the two masses. We use exponentially small asymptotics to derive the long-time ODE's that quantify this mass exchange. Our theory is validated using full numerical simulations of the original model- of both the original stochastic particle system and its PDE limit. Our formal computations show that adding noise destroys the degeneracy in the equilibrium solution and leads to a unique symmetric steady state.
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