Waves in Periodic and Random Media

By Peter Kuchment. 2003

221 citations recorded by the source corpus.

Subfields: Atmospheric Science, Mechanics of Materials, Oceanography

View Paper: https://www.semanticscholar.org/paper/877085292aa64d29b01b73bd4490e547dfe006c6

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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.”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “The study of reactiondiffusion equations in space-periodic media goes back to Freidlin [11] and Freidlin and Gartner[12].”
Existence and uniqueness of the solution of a space–time periodic reaction–diffusion equation (2010, background): “In 1979, Freidlin and Gartner were the first to investigate the heterogeneous equation in [15].”
Inverse spectral problem for quantum graphs (2006, background): “One can find a recent reference list with historical remarks in the book [2] and volumes [25, 26] devoted entirely to quantum graphs.”
Propagation Phenomena for A Reaction–Advection–Diffusion Competition Model in A Periodic Habitat (2014, unknown): “More specifically, Gätner and Friedlin [7, 8] studied the spreading speed for an equation of Fisher type in which the mobility and the growth function vary periodically in space via probabilistic methods.”
Front propagation in periodic excitable media (2002, methodology): “The homogenization limit ε → 0 has been carried out by Freidlin [37], [38], Heinze [51] and Xin [107].”
The speed of propagation for KPP type problems. I: Periodic framework (2005, methodology): “2) without advection in the whole space R with periodic coefficients was considered in the important work of G ärtner and Freidlin [39] and later by Freidlin [34] in the case with advection q (the proofs in [39] and [34] used probabilistic tools).”
Spreading Properties and Complex Dynamics for Monostable Reaction–Diffusion Equations (2012, unknown): “in the sense that, as t→ +∞, u(t, c t e+ z)→ 1 for any 0 ≤ c < C∗(e) and u(t, c t e+ z)→ 0 for any c > C∗(e) locally uniformly in z such that c t e+ z ∈ Ω (see [5, 13, 14, 28, 41]).”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “Using heuristics and numerical simulations, in a one-dimensional situation and for the particular nonlinearity f (x,u) := u(η(x)−μu), Shigesada, Kawasaki and Teramoto were able to recover earlier results on the minimal speed of spreading obtained by probabilistic methods by Gärtner and Freidlin [34,”
Asymptotic spreading in heterogeneous diffusive excitable media (2008, background): “This theorem has first been proved in space periodic media by Freidlin and Gärtner [16] and Freidlin [15].”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, methodology): “Such a result is already known when the full nonlinearity f (and not only its derivative near u = 0) is a random stationary ergodic function since the pioneering work of Freidlin and Gartner [16].”
The speed of propagation for KPP type problems. II (2010, background): “Namely, for problem (1.3) under the assumption that 0 f(x, s) ≤ f ′s(x, 0)s for all s ∈ (0, 1) and x ∈ Ω, Freidlin and Gärtner [14] and Freidlin [13] in the case of RN , and then Weinberger [40] in the general periodic framework described above, proved the existence of an asymptotic spreading spe”