Annihilation of two interfaces in a hybrid system
Pages: 857  869,
Issue 5,
October
2015
doi:10.3934/dcdss.2015.8.857 Abstract
References
Full text (954.7K)
Related Articles
ShinIchiro Ei  Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita ward, Sapporo, 0600810, Japan (email)
Kei Nishi  Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita ward, Sapporo, 0600810, Japan (email)
Yasumasa Nishiura  WPI Advanced Institute for Materials Research, Tohoku University, 211 Katahira, Aobaku, Sendai 9808577, Japan (email)
Takashi Teramoto  Asahikawa Medical University, 2111, Midorigaokahigashi, Asahikawa 0788510, Japan (email)
1 
M. Argentina, P. Coullet and V. Krinsky, Headon collisions of waves in an excitable FitzHughNagumo system: a transition from wave annihilation to classical wave behavior, J. theor. Biol., 205 (2000), 4752. 

2 
M. Argentina, P. Coullet and L. Mahadevan, Colliding waves in a model excitable medium: Preservation, annihilation, and bifurcation, Phys. Rev. Lett., 79 (1997), 28032806. 

3 
X. Chen, S.I. Ei and M. Mimura, Selfmotion of camphor discs. Model and analysis, Networks and Heterogeneous Media, 4 (2009), 118. 

4 
S.I. Ei, The motion of weakly interacting pulses in reactiondiffusion systems, J. Dyn. Diff. Eq., 14 (2002), 85137. 

5 
S.I. Ei, H. Ikeda and T. Kawana, Dynamics of front solutions in a specific reactiondiffusion system in one dimension, Jpn. J. Indust. Appl. Math., 25 (2008), 117147. 

6 
S.I. Ei, M. Mimura and M. Nagayama, Pulsepulse interaction in reactiondiffusion systems, Physica D, 165 (2002), 176198. 

7 
P. C. Fife, Dynamics of Internal Layers and Diffusive Interface, 1st edition, Society for Ind. and Appl. Math., Pennsylvania, 1988. 

8 
Y. Fukao, Y. Morita and H. Ninomiya, Some entire solutions of the AllenCahn equation, Taiwanese J. Math., 8 (2004), 1532. 

9 
H. Ikeda, T. Ikeda and M. Mimura, Hopf bifurcation of travelling pulses in some bistable reactiondiffusion systems, Methods and Appl. of Anal., 7 (2000), 165193. 

10 
Y. Kuramoto, Instability and turbulence of wavefronts in reactiondiffusion systems, Prog. Theor. Phys., 63 (1980), 18851903. 

11 
Y. Morita and Y. Mimoto, Collision and collapse of layers in a 1D scalar reactiondiffusion equation, Physica D, 140 (2000), 151170. 

12 
K. Nishi, Y. Nishiura and T. Teramoto, Dynamics of two interfaces in a hybrid system with jumptype heterogeneity, Jpn. J. Ind. App. Math., 30 (2013), 351395. 

13 
Y. Nishiura, T. Teramoto and K.I. Ueda, Scattering and separators in dissipative systems, Phys. Rev. E, 67 (2003), 05621010562107. 

14 
Y. Nishiura, T. Teramoto and K.I. Ueda, Scattering of traveling spots in dissipative systems, Chaos, 15 (2005), 047509, 10pp. 

15 
T. Ohta, M. Mimura and R. Kobayashi, Higherdimensional localized patterns in excitable media, Physica D, 34 (1989), 115144. 

16 
A. Scheel and J. Wright, Colliding dissipative pulses  the shooting manifold, J. Diff. Eqs., 245 (2008), 5979. 

17 
H. Yagisita, Backward global solutions characterizing annihilation dynamics of travelling fronts, Publ. RIMS, Kyoto Univ., 39 (2003), 117164. 

Go to top
