4 papers
Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
Keisuke Matsuya, Masahiro Kanai
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time ver…
Mathematical Modelings for Angiogenesis - A Cellular Automaton Model and its Continuous Model
Keisuke Matsuya, Hiroki Kurihara, Tetsuji Tokihiro
Based on recent experiments with time-lapse fluorescent imaging, we propose a cellular automaton model for the dynamics of vascular endothelial cells (ECs) in angiogenic morphogene…
Blow-up of solutions to a Dirichlet problem for the discrete semi-linear heat equation
Keisuke Matsuya
In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizi…
The blow-up theorem of a discrete semilinear wave equation
Keisuke Matsuya
In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear…