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- Masato Iida, Masayasu Mimura, Hirokazu Ninomiya
- Journal of mathematical biology
- 2006

The cross-diffusion competition systems were introduced by Shigesada et al. [J. Theor. Biol. 79, 83-99 (1979)] to describe the population pressure by other species. In this paper, introducing the densities of the active individuals and the less active ones, we show that the cross-diffusion competition system can be approximated by the reaction-diffusion… (More)

This paper is concerned with the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. First we show that if the convex hull of the image of initial data does not intersect the positive real axis, then the solution exists globally in time and converges to the trivial steady state.… (More)

We are dealing with a reaction-diffusion equation ut = ∆u+uyy+f(u) in R , where (x, y) = (x1, . . . , xn, y) ∈ R n+1 and ∆ is the Laplacian in R. Suppose that the equation has a bistable nonlinearity, namely it has two stable constant solutions u = 0, 1 and an unstable one between those. With the unbalanced condition ∫ 1 0 f(u)du > 0 the equation allows… (More)

This paper deals with entire solutions of a bistable reaction-diffusion equation for which the speed of the traveling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two traveling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a… (More)

In this paper we consider a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion under zero Dirichlet boundary condition. By using topological degree theory, bifurcation theory, energy estimates and asymptotic behavior analysis, we prove the existence, uniqueness and multiplicity of positive steady states… (More)

- Ian Johnson, Evelyn Sander, +4 authors THOMAS WANNER
- 2013

Diblock copolymers are a class of materials formed by the reaction of two linear polymers. The different structures taken on by these polymers grant them special properties, which can prove useful in applications such as the development of new adhesives and asphalt additives. We consider a model for the formation of diblock copolymers first proposed by Ohta… (More)

- Masato Iida, Roger Lui, Hirokazu Ninomiya
- SIAM J. Math. Analysis
- 2011

Long-time asymptotic properties of the solutions of the system ut = f(u), where f(u) is positive homogeneous of degree p > 1, are studied. We also consider the corresponding linearly perturbed system ut = f(u) +Au. It is shown that if A = αI, then the global existence of all solutions for one value of α implies that the same property holds for all α, and… (More)

This paper examines the following question: Suppose that we have a reaction-diffusion equation or system such that some solutions which are homogeneous in space blow up in finite time. Is it possible to inhibit the occurrence of blow-up as a consequence of imposing Dirichlet boundary conditions, or of other effects where diffusion plays a role? We give… (More)

- Yoshitaro Tanaka, Hiroko Yamamoto, Hirokazu Ninomiya
- Development, growth & differentiation
- 2017

In recent years, spatial long range interactions during developmental processes have been introduced as a result of the integration of microscopic information, such as molecular events and signaling networks. They are often called nonlocal interactions. If the profile of a nonlocal interaction is determined by experiments, we can easily investigate how… (More)