2007
DOI: 10.1007/s00033-007-7005-y
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Abstract: This paper is concerned with the travelling wave fronts of nonlocal reaction-diffusion systems with delays. The existence of travelling wave fronts for nonlocal reaction-diffusion systems with delays is established by using Schauder's fixed point theorem and upper-lower solution technique. Then these results are applied to the nonlocal delayed Logistic model and the delayed Belousov-Zhabotinskii reaction-diffusion system. Our results show that the time delay can reduce the minimal wave speed while the nonlocal… Show more

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Cited by 125 publications
(69 citation statements)
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“…In literature, the corresponding propagation theory of nonlocal dispersal models (1.1) and (1.2) has been widely S. PAN studied, and most results are indexed by the traveling wave solutions and asymptotic speed of spreading. We refer to Bates et al [2], Carr and Chmaj [3], Chen [4], Coville and Dupaigne [5,6], Jin and Zhao [9], Li et al [10], Pan [14], Pan et al [15,16], Shen and Zhang [17], Sun et al [20], Wu and Liu [21], Xu and Weng [23], Zhang et al [26], Zhang et al [27] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
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“…In literature, the corresponding propagation theory of nonlocal dispersal models (1.1) and (1.2) has been widely S. PAN studied, and most results are indexed by the traveling wave solutions and asymptotic speed of spreading. We refer to Bates et al [2], Carr and Chmaj [3], Chen [4], Coville and Dupaigne [5,6], Jin and Zhao [9], Li et al [10], Pan [14], Pan et al [15,16], Shen and Zhang [17], Sun et al [20], Wu and Liu [21], Xu and Weng [23], Zhang et al [26], Zhang et al [27] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…and the discussion in Sections 2-4 can be similarly applied to such a monotone condition, see Pan et al [15].…”
Section: Introductionmentioning
confidence: 99%
“…Недавно в работе [6] было рассмотрено уравнение (1.1) с квазимонотонной функцией f и установлено существование фронта бегущей волны с помощью теоремы Шаудера о неподвижной точке и техники суб-и суперрешений. В [7] методами работы [8] изучалась устойчивость фронтов быстро движущихся волн уравнения (1.1), где f (u, v) = −au + bv(1 − u), т. е. уравнения u t − J * u + u + au = bu(x, t − τ )(1 − u), b > a 0, ( В настоящей работе по-новому рассматривается устойчивость фронтов бегу-щих волн для уравнения (1.1), где f (u, v) = −au + bv(1 − u), и мы не налагаем ограничения (1.4).…”
Section: § 1 введениеunclassified
“…В процессе написания работы выяснилось, что Р. Хуан с соавторами [24] рассмотрели задачу 6) где f α определяется, как в (1.5), и показали устойчивость плоских волн для этой задачи с помощью преобразования Фурье и принципа сравнения при условии, что…”
Section: § 1 введениеunclassified
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