Front Propagation in Heterogeneous Media

By J. Xin. SIAM Review, 2000

528 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e6de2d2bf84c8a30b4b031c7381f3a6d46495525

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Citations in the corpus

Spreading speeds for a two-species competition-diffusion system (2018, unknown): “In general, we refer to [25] for results on travelling waves in physics and biology, and to [26] for a review of this field of research.”
The speed of propagation for KPP type problems. I: Periodic framework (2005, methodology): “The case of the whole spaceRN with periodic diffusion and advection was first considered by Xin [91], [93] for a combustion-type nonlinearityf satisfying (1.10), for which the speed of propagation of the pulsating fronts was proved to be unique in any given direction.”
A diffusive logistic model with a free boundary in time-periodic environment☆ (2013, background): “These results have been extended to higher dimensions in [2], and extensive further development on traveling wave solutions and the spreading speed has been achieved in several directions, in particular, to situations of various heterogeneous environments; see, for example, [3, 4, 5, 6, 25, 32, 33] ”
Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion (2004, background): “There is also a survey paper of Xin [ 30 ] and a textbook of Volpert et al . [26].”
STABILITY OF TRAVELLING WAVES WITH ALGEBRAIC DECAY FOR n-DEGREE FISHER-TYPE EQUATIONS (2006, background): “There are some other detailed stability results (see [29, 24, 25, 14] and references therein) on the travelling waves with critical and non-critical speed, which imply that the exponential decay rate of the initial data at +∞ determines the asymptotic behavior of the solution.”
Stability of strong travelling waves for a non-local time-delayed reaction–diffusion equation (2008, background): “For partial differential equations without time delays, including reaction–diffusion equations, travelling waves have been extensively studied; see, for example, the pioneering works [6, 20] and other more recent contributions [1–3, 7–14, 18–20, 30, 31], and the references therein (see also [28] and”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “We refer to [21, 6, 34, 35] for nonlocal dispersal equations, and two survey papers [43, 15] for more references.”
Propagation Phenomena for A Reaction–Advection–Diffusion Competition Model in A Periodic Habitat (2014, unknown): “, [35] and references therein.”
Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ (2011, background): “These results have been extended to higher dimensions in [2], and extensive further development on traveling wave solutions and the spreading speed has been achieved in several directions; we refer to [30, 13, 28, 3, 4, 17, 29] and the references therein for more details.”
Chapter 18 - Stability of Travelling Waves (2002, methodology): “We refer to the recent review [184] and to the monograph [182] for many other references related to the existence and stability of waves.”
Bistable Traveling Waves for Monotone Semiflows with Applications (2011, methodology): “1) under appropriate conditions so that the existence result in [43, 42] is improved (see the details in Subsection 6.”
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations (2011, background): “See, for example, [3], [4], [5], [10], [16], [24], [25], [26], [31], [33], [46], [47], and references therein for space and/or time periodic reaction diffusion equations of KPP type, see [7], [10], [13], [32], [34], [35], [36], [48], [49], and references therein for KPP models in random media, and s”
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary (2010, unknown): “These results have been extended to higher dimensions in [2], and extensive further development on traveling wave solutions and the spreading speed has been achieved in several directions; we refer to [30, 13, 28, 3, 4, 17, 29] and the references therein for more details.”