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arXiv · 2307.16436

Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case

Clarissa Astuto·Jan Haskovec·Peter Markowich·Simone Portaro
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Abstract

We study self-regulating processes modeling biological transportation networks as presented in \cite{portaro2023}. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $D$. We explore systematically various scenarios and gain insights into the behavior of $D$ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $D$ touches zero, confirming the previous hints of local existence in particular cases.

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Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro. 2023-07-31. Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case. https://arxiv.org/abs/2307.16436

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