6 citations · 11 across the 14 of their papers we have counts for
14 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…
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…
Impact of topography and combustion functions on fire front propagation in an advection-diffusion-reaction model for wildfires
Luca Nieding, Cordula Reisch, Dirk Langemann +1
Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely use…
Towards Model Discovery Using Domain Decomposition and PINNs
Tirtho S. Saha, Alexander Heinlein, Cordula Reisch
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The…
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…
Studying wildfire fronts using advection-diffusion-reaction models
Koondanibha Mitra, Qiyao Peng, Cordula Reisch
In this work, we study the propagation of wildfires using an advection--diffusion--reaction model which also includes convective and radiative heat loss. An existing model is discu…
Building up a model family for inflammations
Cordula Reisch, Sandra Nickel, Hans-Michael Tautenhahn
The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of…
Model selection focusing on longtime behavior of differential equations
Cordula Reisch, Hannah Burmester
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms o…
Analytical and numerical insights into wildfire dynamics: Exploring the advection-diffusion-reaction model
Cordula Reisch, Adrián Navas-Montilla, Ilhan Özgen-Xian
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understand…
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…
Longterm existence of solutions of a reaction diffusion system with non-local terms modeling an immune response -- an interpretation-orientated proof
Cordula Reisch, Dirk Langemann
This paper shows the global existence and boundedness of solutions of a reaction diffusion system modeling liver infections. The existence proof is presented step by step and the f…
Sensitivity Analysis for Vehicle Dynamics Models -- An Approach to Model Quality Assessment for Automated Vehicles
Marcus Nolte, Richard Schubert, Cordula Reisch +1
Model-based approaches have become increasingly popular in the domain of automated driving. This includes runtime algorithms, such as Model Predictive Control, as well as formal an…