教師資料查詢 | 類別: 期刊論文 | 教師: 楊定揮YANG, TING-HUI (瀏覽個人網頁)

標題:Diversity of traveling wave solutions in FitzHugh–Nagumo type equations
學年98
學期1
出版(發表)日期2009/08/01
作品名稱Diversity of traveling wave solutions in FitzHugh–Nagumo type equations
作品名稱(其他語言)
著者Hsu, Cheng-hsiung; 楊定揮; Yang, Ting-hui; Yang, Chi-ru
單位淡江大學數學學系
出版者Elsevier
著錄名稱、卷期、頁數Journal of Differential Equations 247(4), pp.1185-1205
摘要In this work we consider the diversity of traveling wave solutions of the FitzHugh–Nagumo type equations ut=uxx+ƒ(u, w), Wt=εg(u, w), where f(u,w)=u(u−a(w))(1−u) for some smooth function a(w) and g(u,w)=u−w. When a(w) crosses zero and one, the corresponding profile equation possesses special turning points which result in very rich dynamics. In [W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh–Nagumo type equations, J. Differential Equations 225 (2006) 381–410], Liu and Van Vleck examined traveling waves whose slow orbits lie only on two portions of the slow manifold, and obtained the existence results by using the geometric singular perturbation theory. Based on the ideas of their work, we study the co-existence of different traveling waves whose slow orbits could involve all portions of the slow manifold. There are more complicated and richer dynamics of traveling waves than those of [W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh–Nagumo type equations, J. Differential Equations 225 (2006) 381–410]. We give a complete classification of all different fronts of traveling waves, and provide an example to support our theoretical analysis.
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語言英文
ISSN0022-0396
期刊性質國外
收錄於SCI
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