Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity

By François Hamel. 2008

145 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/881cb3eeca9e617db5fa28aac1d9067d84c4f6a6

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In Computer Networks and Communications

In Control and Systems Engineering

In Public Health, Environmental and Occupational Health

Citations in the corpus

Critical travelling waves for general heterogeneous one-dimensional reaction–diffusion equations (2015, unknown): “As α 7→ k(α) is convex (see [12]), α > 0 and c < c, simple graphical considerations yield that αc < αc′ .”
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.”
The speed of propagation for KPP type problems. II (2010, background): “2)) and on A and q, existence and uniqueness (for each speed) of pulsating fronts for, and only for, speeds c ≥ c∗(e) were proved in [4, 7, 20, 21].”
Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, unknown): “[16] F. Hamel, Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity, J. Math.”
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.”
Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat (2014, methodology): “Furthermore, some variational formulas for cL in the positive case and in the more specific KPP case have been derived in [10, 12, 20] and some further qualitative and uniqueness properties for each speed c ∈ [cL,+∞) have been given in [25, 28, 29].”
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).”
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations (2011, background): “2) have been well extended to general time and space independent monostable equations (see [1], [2], [6], [12], [22], [39], [45], etc.”
Uniqueness and stability properties of monostable pulsating fronts (2011, methodology): “Before doing so, we first quote from [20] a useful lemma (see Lemma 2.3 in [20]) which is a comparison result between sub-and super-solutions in the region where s ≤ h. Lemma 2.1 Let ρ ∈ (0, min Ω (p + − p − )) be given as in (1.5).”