7 papers · 1 filter
Asynchronous exponential growth for structured population models in measure space
Christian Düll, József Z. Farkas, Piotr Gwiazda +1
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop co…
Multiple diffusion scales and diffusion-driven instability: Emergence of near- and far-from-equilibrium patterns
Théo André, Szymon Cygan, Anna Marciniak-Czochra +1
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusio…
Statistical parameter identification of mixed-mode patterns from a single experimental snapshot
Alexey Kazarnikov, Robert Scheichl, Irving R. Epstein +2
Parameter identification in pattern formation models from a single experimental snapshot is challenging, as traditional methods often require knowledge of initial conditions or tra…
Structured Population Models on Polish spaces: A unified Approach including Graphs, Riemannian Manifolds and Measure Spaces to describe Dynamics of Heterogeneous Populations
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent…
Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…
Instability of all regular stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch +1
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the conte…