2 citations · 3 across the 5 of their papers we have counts for
7 papers
Tools for stability analysis of fractional reaction diffusion systems
Sofwah Ahmad, Szymon Cygan, Grzegorz Karch
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of sol…
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…
Discontinuous stationary solutions to certain reaction-diffusion systems
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied…
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…
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…