1 citations · 1 across the 1 of their papers we have counts for
4 papers
Solutions at vacuum and rarefaction waves in pressureless Euler alignment system
Szymon Cygan, Grzegorz Karch
We construct global-in-time weak solutions to the pressureless Euler alignment system posed on the whole line and supplemented with initial conditions, where an initial density 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…
Stability of constant steady states of a chemotaxis model
Szymon Cygan, Grzegorz Karch, Krzysztof Krawczyk +1
The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole -dimensional space is studied. For this model, every constant is a stationary…
Pattern formation in nonlocal Kondo model
Szymon Cygan
We study a nonlocal evolution equation generalising a model introduced by Shigeru Kondo to explain colour patterns on a skin of a guppy fish. We prove the existence of stationary s…