Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

By Xinfu Chen, Jong-Shenq Guo. 2003

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/c9e46c9f829bea6275c47750f9c4315c01671acc

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In Applied Mathematics

In Geometry and Topology

In Public Health, Environmental and Occupational Health

Citations in the corpus

Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats (2010, unknown): “Note that in [10], [11], [24], [30], [56], [61], etc.”
Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects (2008, methodology): “In fact, these types of supersolutions and subsolutions were firstly used by Chen and Guo ([12], Lemma 3.7).”
Existence and nonexistence of traveling waves for a nonlocal monostable equation (2008, background): “, [5, 7, 10, 11, 12, 13, 14, 15, 18, 19, 23, 24, 26, 27, 28] on traveling waves and long-time behavior in various monostable evolution systems, [2, 4, 30] nonlocal bistable equations and [20] Euler equation.”
Existence, uniqueness and stability of travelling waves in a discrete reaction–diffusion monostable equation with delay (2005, background): “Guo [7, 8 ] discussed a more general class of system”
Existence, Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable Equations (2011, background): “... [2–4,8,11,17,24,25,42, 43,45,46,57], and references therein for more general time and space independent reaction diffusion equations of KPP type; see [5–7,14,21,27,29,32,36,37,40,44,67], and references therein for space and/or time periodic reaction diffusion equations of KPP type; see [14,18, 3”
Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases (2007, unknown): “This construction extends known results on the existence of travelling wave in discrete system, see for example [11, 13, 27].”
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity (2012, methodology): “In order to obtain the detailed asymptotic behavior of φ(ξ) as ξ → −∞, we follow the ideas of Chen and Guo [13] and Chen, Fu and Guo [14], and begin with the following equation cu′(x) = ∫ R J (y)u(x − y)dy + bu(x), x ∈R, (3.4) where b, c are constants and c > 0.”
Front propagation for discrete periodic monostable equations (2006, background): “For related works to (1.2) on homogeneous discrete media with monostable or bistable nonlinearities, we refer the readers to [5, 6 , 7, 14, 25, 26] and the references cited therein.”
Uniqueness of travelling waves for nonlocal monostable equations (2004, methodology): “In this work we extend the method of Diekmann and Kaper to obtain a similar, complete result such as the one in [5].”
On uniqueness of semi-wavefronts (2010, background): “2 Nonlocal lattice equations [6,16,26,30,41] Now we consider semi-wavefronts wj(t) = u(j + ct), u(−∞) = 0, of the nonlocal lattice equation dwj(t) dt = D[wj+k(t)− wj(t)]− dwj(t) + ∑”
Nonlocal anisotropic dispersal with monostable nonlinearity (2008, background): “Then, Harris, Hudson and Zinner [18] and more recently Carr and Chmaj [4], Chen and Guo [5] and Coville and Dupaigne [11] extended and completed the work of Schumacher to more general monostable nonlinearities and dispersal kernels J satisfying what is called in the literature the Mollison condition”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, unknown): “The reader is referred to [7], [8], [9], [21], [22], [29], [50], [59], [60].”
Existence and uniqueness of traveling waves for non-monotone integral equations with applications (2010, methodology): “[4] X. Chen, J.S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math.”