644 citations · 1.5k across the 50 of their papers we have counts for
60 papers
Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case
Clarissa Astuto, Jan Haskovec, Peter Markowich +1
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 Neuma…
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
Asymmetry and condition number of an elliptic-parabolic system for biological network formation
Clarissa Astuto, Daniele Boffi, Jan Haskovec +2
We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network formation. The numerical method is based on a non-linear finite…
Comparison of two aspects of a PDE model for biological network formation
Clarissa Astuto, Daniele Boffi, Jan Haskovec +2
We compare the solutions of two systems of partial differential equations (PDE), seen as two different interpretations of the same model that describes formation of complex biologi…
Emergence of biological transportation networks as a self-regulated process
Jan Haskovec, Peter Markowich, Simone Portaro
We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal -gradient flow for the symmetric tensor valued diffusivity of…
Tensor PDE model of biological network formation
Jan Haskovec, Peter Markowich, Giulia Pilli
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of t…