Asymptotic spreading in heterogeneous diffusive excitable media

By Henri Berestycki, François Hamel, Grégoire Nadin. 2008

182 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/cdf54b32a32e19e0d084a0cee705c5fe0bdccfe5

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Citations in the corpus

Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ (2011, result): “These results have been extended to higher dimensions in [2], and further related research may be found, for example, in [3, 4, 5, 14, 20, 29, 30] and the references therein.”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, background): “Indeed, if u0 is a non-null initial datum such that 0 ≤ u0 ≤ 1, then by (7) and (9) the solution u = u(t, x) of (1) converges to 1 as t → +∞ locally in x ∈ R [3, 7].”
Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats (2013, background): “For spreading properties, the reader is referred to [38] for homogeneous equations, to [2], [15], [16], and [39] for periodic equations, and to [2], [4] for general equations.”
Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients (2015, background): “In the case where the coefficients are periodic in time too, the class of admissible speeds has been characterized by the first author in [16] (see also [6]).”
Dynamics for a diffusive prey-predator model with different free boundaries (2015, methodology): “Since these intervals [k, k+2] overlap and C is independent of k, it follows that ‖u‖C0,1([1,3]×[0,[g(n+1)]−1]) ≤ C.”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “Furthermore, they have showed that there exists a critical speed c∗ so that a pulsating front with speed c ≥ c∗ in the direction e connecting the two equilibria 0 and p(x) exists and no pulsating front with speed c c∗ exists.”
Existence and uniqueness of the solution of a space–time periodic reaction–diffusion equation (2010, background): “In [3], Berestycki, Hamel and the author prove spreading behaviors and compute the spreading speed of a solution with compactly supported initial datum with the help of the periodic principal eigenvalues (kα)α .”
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] ”