Analysis of the periodically fragmented environment model: II—biological invasions and pulsating travelling fronts

By Henri Berestycki, François Hamel, Lionel Roques. 2005

330 citations recorded by the source corpus.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/17edd8bf86168a3cc17e59c7f3c41978eb3ba626

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Citations in the corpus

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].”
Traveling Waves in Discrete Periodic Media for Bistable Dynamics (2008, background): “[5], Berestycki et al. [6], Berestycki et al. [7, 8 ], and Matano [34] for various heterogeneous media.”
Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity (2008, background): “With the condition μ0 < 0, the existence of pulsating fronts in any direction e was proved in [7] for all (and only all) speeds c ≥ c(e), where c(e) is still given by (1.”
Uniqueness and stability properties of monostable pulsating fronts (2011, neutral): “In [7], nonlinearities f = f (x, s) (for x ∈ Ω = R N ) satisfying    p − = 0, f (x, 0) = 0, u → f (x, u) u is decreasing in u > 0, ∃ M > 0, ∀ x ∈ R N , ∀ u ≥ M, f (x, u) ≤ 0 (1.13) were considered, with no advection (q = 0).”
Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients (2015, background): “1999], space-periodic [Berestycki and Hamel 2002; Berestycki et al. 2005; Xin 1992], space-time periodic [Nolen et al.”
On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators (2010, background): “6) and their properties, we follow and adapt the arguments developed in [5, 6, 20].”
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] ”
Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait (2012, background): “Travelling front solutions in heterogeneous versions of (2) with periodicity in space, in time, or more general media are studied in [12], [28], [44], [6], [8], [36], [37].”
Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions (2016, neutral): “According to [6,41] and similarly to the previous model, a necessary and sufficient condition of species survival writes γ (μ) < 0, where γ (μ) denotes the principal eigenvalue associated with the elliptic problem {− ψ = (μ(x) + γ )ψ in ∂nψ + βψ = 0 on ∂ .”
Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats (2013, background): “About existence of traveling waves and characterization of their speeds, the reader is referred to [3], [5] for space periodic equations, and to [27], [29], [30], [39] for space-time periodic equations.”