SELF-REGULATED BIOLOGICAL TRANSPORTATION STRUCTURES WITH GENERAL ENTROPY DISSIPATIONS, PART I: THE 1D CASE

Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study self-regulating processes modeling biological transportation networks as presented in [15]. 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.

Original languageEnglish (US)
Pages (from-to)76-99
Number of pages24
JournalJournal of Dynamics and Games
Volume11
Issue number1
DOIs
StatePublished - 2024

Keywords

  • biology network formation
  • IMEX
  • ODE analysis
  • Runge-Kutta
  • Self-regulating processes
  • well-posedness

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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