Spreading speeds and uniqueness of traveling waves for a reaction diffusion equation with spatio-temporal delays

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• 作者：Zhaoquan Xu ^{xuzhqmaths@126.com" class="auth_mail" title="E-mail the corresponding author} ; Dongmei Xiao ; ¹ ; ^{xiaodm@sjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35K57 ; 35R10 ; 92D25
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 January 2016
• 年：2016
• 卷：260
• 期：1
• 页码：268-303
• 全文大小：456 K

文摘

A class of reaction diffusion equation with spatio-temporal delays is systematically investigated. When the reaction function of this equation is nonlinear without monotonicity, it is shown that there exists a spreading speed c^鈦?/sup>>0$c^{鈦?/mo>}>0$ for this equation such that c^鈦?/sup>$c^{鈦?/mo>}$ is linearly determinate and coincides with the minimal wave speed of traveling waves, and that this equation admits a unique traveling wave (up to translation) with speed c>c^鈦?/sup>$c>c^{鈦?/mo>}$ and no traveling wave with c<c^鈦?/sup>$c<c^{鈦?/mo>}$.