Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion
RC Fetecau, M Kovacic, I Topaloglu - arXiv preprint arXiv:1711.03622, 2017 - arxiv.org
RC Fetecau, M Kovacic, I Topaloglu
arXiv preprint arXiv:1711.03622, 2017•arxiv.orgWe 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 …
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 …
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).
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