87 citations · 396 across the 37 of their papers we have counts for
6 papers · 2 filters
Pattern formation in a diffusion-ODE model with hysteresis
Anna Marciniak-Czochra, Madoka Nakayama, Izumi Takagi
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion…
Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance
P. Gwiazda, J. Jabłoński, A. Marciniak-Czochra +1
Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool…
Dynamical spike solutions in a nonlocal model of pattern formation
Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch +1
Coupling a reaction-diffusion equation with ordinary differential equations (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffus…
Spike patterns in a reaction-diffusion-ode model with Turing instability
Steffen Härting, Anna Marciniak-Czochra
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such sy…
A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium
Anna Marciniak-Czochra, Andro Mikelic
We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous med…
Instability of Turing patterns in reaction-diffusion-ODE systems
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such s…