On uniqueness and monotonicity of solutions of non-local reaction diffusion equation

By Jérôme Coville. 2006

94 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/a95e13cb39807c21800cedb86023ef584cc71485

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Citations in the corpus

Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats (2012, background): “As the movements and interactions of many species in biology and ecology can occur between nonadjacent spatial locations, nonlocal dispersal has also been used to model the population spreading dynamics of species by many people (see [2], [7], [8], [9], [11], [12], [16], [22], [23], [26], and the re”
On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators (2010, unknown): “where Ω ⊂ R, k ≥ 0 satisfies ∫ Rn k(y, x)dy < ∞ for all x ∈ R and b(x) ∈ C(Ω); see among other references [1, 2, 3, 10, 11, 12, 14, 15, 16, 19, 22, 23, 24, 33, 34, 39].”
Nonlocal anisotropic dispersal with monostable nonlinearity (2008, methodology): “Our proof follows ideas of [8] and is mainly based on the sliding methods introduced by Berestycki and Nirenberg [3].”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, background): “See, for example, [11], [13], [15], [36], [41], [45], [57], [58], for the study of entire solutions and the existence of spreading speeds and traveling wave solutions connecting the trivial solution u = 0 and a nontrivial positive stationary solution for some special cases of (1.”
Criteria for the Existence and Lower Bounds of Principal Eigenvalues of Time Periodic Nonlocal Dispersal Operators and Applications (2012, unknown): “The reader is referred to [5,8,10,11,13,15,16,19,20,22,24–26,28,32], etc.”
Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats (2010, unknown): “See, for example, [15], [16], [18], [54], [55] for the study of the existence of spreading speeds and traveling wave solutions connecting the trivial solution u = 0 and a nontrivial positive stationary solution.”
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity (2012, background): “1) with degenerate monostable nonlinearity, the lack of knowledge about asymptotic behavior at −∞ implies that the uniqueness of traveling wave solution is still an open problem (see [15]).”
Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases (2007, unknown): “In particular, the proof relies on the following nonlinear comparison principle that was established in [14]: 32 ha l-0 06 96 20 8, v er si on 1 11 M ay 2 01 2”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “1) we quote [1,2,18,20,21,23,25] for the existence and characterization of traveling fronts for this equation with homogeneous nonlinearity and [3,22,24,36,42] for the study of the stationary problem.”
Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats (2013, background): “See, for example, [8] and [12] for the study of traveling waves of (1.”
Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, background): “) Models similar to (44) and related models for interacting species have been studied by various researchers; see [4, 20, 26, 27, 28, 29, 47, 53, 55] and the references in those papers.”
On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications (2013, unknown): “The reader is referred to [1], [2], [4], [5], [6], [7], [8], [10], [11], [16], [22], [23], [24], [26], [28], [30], [32], etc.”