Calculus of Variations and Geometric Measure Theory

Razvan C. Fetecau - M. Kovacic - I. Topaloglu

Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2017

ArXiv: 1711.03622 PDF


We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of energy minimizers in this limit. Numerical simulations that support the analytical results are presented. A second key scope of the numerical studies is to demonstrate that adding small nonlinear diffusion rectifies a flaw of the plain aggregation model in domains with boundaries, which is to evolve into unstable equilibria (non-minimizers of the energy).