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<p>In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our analysis is a family of energy evolution equations and their dissipation structures, which are novel and of independent interest. This strategy allows us to consider a larger family of pressure laws as well as proving the joint limit, from a compressible Brinkman’s model to the incompressible Darcy’s law, where the latter is a Hele-Shaw type free boundary problem.</p>

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On the Singular Limit of Brinkman’s Law to Darcy’s Law

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Noemi David,
  • Matt Jacobs,
  • Inwon Kim

摘要

In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our analysis is a family of energy evolution equations and their dissipation structures, which are novel and of independent interest. This strategy allows us to consider a larger family of pressure laws as well as proving the joint limit, from a compressible Brinkman’s model to the incompressible Darcy’s law, where the latter is a Hele-Shaw type free boundary problem.