JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 19(3) 457-465 2013年3月 [査読有り]
In this paper, a discretization of a semilinear wave equation whose nonlinear term is a power function is investigated. It is shown that, when a condition on the initial value problem, similar to that governing the existence of blow-up solutions f...
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 31(1) 209-220 2011年9月 [査読有り]
Existence of global solutions to initial value problems for a discrete analogue of a d-dimensional semilinear heat equation is investigated. We prove that a parameter a in the partial difference equation plays exactly the same role as the paramete...
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In this talk, we propose a discretization and an ultradiscretization of Gray-Scott model which is a reaction-diffusion system and whose...
Mathematics for Materials Science and Processing 2016年2月 Institute of Mathematics for Industry
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure preserves the essential properties of the original equation, such as t...