64 citations · 109 across the 12 of their papers we have counts for
8 papers · 1 filter
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan, Grzegorz Karch, Anna Marciniak-Czochra +1
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is…
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…
Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki +1
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only desta…
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…
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…
Unstable patterns in reaction-diffusion model of early carcinogenesis
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by…
Spikes and diffusion waves in one-dimensional model of chemotaxis
Grzegorz Karch, Kanako Suzuki
We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity with a given k…
Blow-up versus global existence of solutions to aggregation equations
Grzegorz Karch, Kanako Suzuki
A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. Optimal conditions on an interaction potential are obtained which lead e…