24 citations · 80 across the 13 of their papers we have counts for
7 papers · 1 filter
Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis
Piotr Biler, Jacek Zienkiewicz
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitab…
Probabilistic approach to quantum separation effect for Feynman-Kac semigroup
Adam Sikora, Jacek Zienkiewicz
Quantum tunnelling phenomenon allows a particle in Schrödinger mechanics tunnels through a barrier that it classically could not overcome. Even the infinite potentials do not alway…
Large global-in-time solutions to a nonlocal model of chemotaxis
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
We consider the parabolic-elliptic model for the chemotaxis with fractional (anomalous) diffusion. Global-in-time solutions are constructed under (nearly) optimal assumptions on th…
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…
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
Piotr Biler, Jacek Zienkiewicz
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than as the initial data is given. This result ha…
Local criteria for blowup in two-dimensional chemotaxis models
Piotr Biler, Tomasz Cieślak, Grzegorz Karch +1
We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solu…
Optimal criteria for blowup of radial and -symmetric solutions of chemotaxis systems
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
A simple proof of concentration of mass equal to for blowing up -symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large is given. Mor…