Spreading speeds and traveling waves for periodic evolution systems

By Xing Liang, Y. Yi, Xiao-Qiang Zhao. 2006

261 citations recorded by the source corpus.

Subfields: Geometry and Topology, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/cd907eb52e2942df9330dcf104dde8d3127a5e2c

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Citations in the corpus

Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats (2012, unknown): “See, for example, [1], [3], [4], [5], [13], [17], [20], [21], [25], [28], [29], [30], [32], [34], [35], [38], [39], [43], [44], [45], and the references therein for the study of the spatial spreading dynamics of (1.”
Existence and nonexistence of traveling waves for a nonlocal monostable equation (2008, background): “, [5, 7, 10, 11, 12, 13, 14, 15, 18, 19, 23, 24, 26, 27, 28] on traveling waves and long-time behavior in various monostable evolution systems, [2, 4, 30] nonlocal bistable equations and [20] Euler equation.”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, methodology): “X.-Q. Zhao’s research is supported in part by the Natural Science and Engineering Research Council of Canada.”
Periodic traveling curved fronts in reaction–diffusion equation with bistable time-periodic nonlinearity (2011, background): “1) have been well studied, see [1,14,20–25] for time-periodic or time almost periodic traveling wave solutions and [3–5,12,13,15,19,28,29] for the autonomous case.”
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity (2012, background): “Recently, by appealing to the theory of asymptotic speeds of spread and traveling waves for monotonic periodic semi-flows [28], Jin and Zhao [26] investigated the spreading speed in a strong sense and”
Fast propagation for KPP equations with slowly decaying initial conditions (2009, background): “Further estimates about the finite spreading speeds associated with compactly supported or exponentially decaying initial conditions have been obtained in [1] for homogeneous equations in R , in [2] for one-dimensional periodic equations, in [6, 24, 29, 35, 41, 43] for higherdimensional equations se”
Traveling waves of diffusive predator-prey systems: Disease outbreak propagation (2012, background): “[38] developed a theory of traveling wave based on some abstract results of Liang and Zhao [39].”
Spreading speeds and travelling waves for non-monotone time-delayed lattice equations (2010, background): “A general theory of spreading speeds and travelling waves has been developed for monotone semiflows (Weinberger 1982; Lui 1989; Li et al. 2005; Liang et al. 2006; Liang & Zhao 2007).”
Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats (2010, unknown): “7) has been widely studied (see [1], [2], [5], [6], [7], [19], [22], [25], [29], [34], [39], [40], [41], [44], [45], [47], [48], [49], [53], [54], [55], and references therein).”
Monotone Wavefronts for Partially Degenerate Reaction-Diffusion Systems (2009, background): “Thus, we may not expect to apply the abstract results developed in [22,7,8] to prove the existence of monostable wavefronts for general partially degenerate systems (1.”
Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, unknown): “[24], Liang and Zhao [25], Nolen and Xin [30], Xin [35], Zhao [36]).”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, unknown): “See, for example, [1], [3], [4], [5], [16], [18], [23], [27], [28], [33], [37], [38], [39], [40], [42], [43], [44], [47], [48], [49], [51], [52], [56], [57], [58], and references therein, for the study of the spatial spread and front propagation dynamics of (1.”
Propagation dynamics for monotone evolution systems without spatial translation invariance (2020, methodology): “This theory has been greatly developed in [13, 14, 17, 27, 28, 29, 30, 39, 42, 44] for more general monotone and some non-monotone semiflows so that it can be applied to a variety of discrete and continuous-time evolution systems in homogeneous or periodic media.”