Propagation speed of travelling fronts in non local reaction–diffusion equations

By Jérôme Coville, Louis Dupaigne. 2005

139 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/067f8062083939f5ac96574a4d7f0f60370f06bf

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Citations in the corpus

A logistic equation with refuge and nonlocal diffusion (2009, background): “We quote for instance [3], [5], [6], [8], [15], [16], [18], [19], [32] and [33], devoted to travelling front type solutions to the parabolic problem when Ω = R, and [4], [9], [10], [17], [31], which dealt with the study of problem (1.”
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources (2006, background): “There is also a number of works where the diffusion term is replaced by convolution (see, e.g., [ 4 ]).”
Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases (2007, unknown): “2) Ut − (J ⋆ U − U) = f(U), where J : R → R is a nonnegative function of mass one and f a given nonlinearity, see for example [4, 18, 17, 23, 28, 30].”
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].”
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.”
On the principal eigenvalue of some nonlocal diffusion problems (2009, background): “Problem (1.2) and its stationary version have been considered recently for several kinds of nonlinearities f. We quote for instance [4], [6], [7], [10], [18], [19], [ 21 ], [22], [32] and [33], devoted to travelling front type solutions to the parabolic problem when › = R, and [5], [11], [12], [20],”
Generalized Transition Waves and Their Properties (2010, unknown): “in [2, 10, 14, 15, 16, 21, 22]).”
Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations (2014, background): “2) are often used to model diffusive systems which exhibit nonlocal internal interactions (see [4, 7, 10, 11, 12, 16, 19, 24, 26], etc.”
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.”
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.”
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.”
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”