64 citations · 109 across the 12 of their papers we have counts for
13 papers
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…
Dispersive estimates for quantum walks on 1D lattice
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We consider quantum walks with position dependent coin on 1D lattice . The dispersive estimate is shown…
Dynamics of solitons for nonlinear quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically \cite{MSSSS18DCDS, MSSSS18QIP}. It was shown that if the nonlinearity is w…
Scattering and inverse scattering for nonlinear quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scatterin…
Weak limit theorem for a nonlinear quantum walk
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
This paper continues the study of large time behavior of a nonlinear quantum walk begun in arXiv:1801.03214. In this paper, we provide a weak limit theorem for the distribution of…
On nonlinear scattering for quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak…
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…