# RDS Seminar

### 第1回 RDSセミナー2012

2012年 4月18日（水） 16:30-17:30

Campus map　in Japanese 　　in English

The Sign of the wave speed for the Lotka-Volterra competition-diffusion system

In this work, we study the traveling front solutions of the Lotka-Volterra competition-diffusion system with bistable nonlinearity. It is well-known that the wave speed of traveling front is unique. Although little is known for the sign of the wave speed. In this paper, we first study the standing wave which gives some criteria when the speed is zero. Then, by the monotone dependence on parameters, we obtain some criteria about the sign of the wave speed under some parameter restrictions.

### RDS Mini-Workshop

2012年 2月1日（水）

Campus map　in Japanese 　　in English

15:00-15:45
Masahikio Shimojo （Meiji Univ.）

"Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity"

16:00-16:45
Jong-Shenq Guo （Tamkang Univ.）

"On a free boundary problem for a two-species weak competition system"

17:00-17:45
Michel Chipot （Zurich Univ.）

"On the asymptotic behavior of variational inequalities set in cylinders"

### 第5回 RDSセミナー2011

2012年 1月30日（月） 17:00-18:00

Campus map　in Japanese 　　in English

### 第4回 RDSセミナー2011

2011年 12月5日（月） 17:00-18:00

Campus map　in Japanese 　　in English

### 第3回 RDSセミナー2011

2011年 11月14日（月） 17:40-18:40

Campus map　in Japanese 　　in English

２種競争系の定常解の分岐構造について

### 第2回 RDSセミナー2011

2011年 11月14日（月） 16:30-17:30

Campus map　in Japanese 　　in English

Active control of pattern formation in excitable systems

Cardiac arrhythmias, a precursor of fibrillation-like states in the beating heart, are associated with spiral waves and spatiotemporal chaos of wave propagation, respectively. Far-fi eld pacing (FFP) also known as wave emission on heterogeneities is a promising method for terminating such waves by using heterogeneities in the tissue as internal pacing sites. This seminar will be a good mix of numerical simulations, theoretical derivatives and experimental verifications. First, I will introduce spiral waves in excitable media and explain exemplarily why spiral wave may stabilize and how spiral waves are terminated generally in real heart. Thereafter, I will introduce FFP with its basic mechanisms and recent related findings.

### 第1回 RDSセミナー2011

2011年 11月7日（月） 17:00-18:00

Multi-dimensional traveling fronts in bistable reaction-diffusion equations

This paper studies traveling front solutions of convex polyhedral shapes in bistable reaction-diffusion equations including the Allen-Cahn equations or the Nagumo equations. By taking he limits of such solutions as the lateral faces go to infinity, we construct a three-dimensional traveling front solution for any given $g\in C^{\infty}(S^{1})$ with $\min_{0\leq \theta\leq 2\pi}g(\theta)=0$.