8 papers
Multiphase cross-diffusion models for tissue structures: modeling, analysis, numerics
Ansgar Jüngel, Cordula Reisch, Sara Xhahysa
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures a…
Recent Analytical and Computational Developments on the Advection-Diffusion-Reaction Wildfire Model
Luca Nieding, A. George Morgan, Adrian Navas +6
Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematic…
Rigorous fast signal diffusion limit and convergence rates with the initial layer effect in a competitive chemotaxis system
Cordula Reisch, Bao-Ngoc Tran, Juan Yang
We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chem…
Turing instability for nonlocal heterogeneous reaction-diffusion systems: A computer-assisted proof approach
Maxime Breden, Maxime Payan, Cordula Reisch +1
This paper provides a computer-assisted proof for the Turing instability induced by heterogeneous nonlocality in reaction-diffusion systems. Due to the heterogeneity and nonlocalit…
Modeling wildfire dynamics through a physics-based approach incorporating fuel moisture and landscape heterogeneity
Adrián Navas-Montilla, Cordula Reisch, Pablo Diaz +1
Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and compu…
Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biology and numerical methods for ODEs
Cordula Reisch, Hendrik Ranocha
We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with…