The speed of propagation for KPP type problems. II

By Henri Berestycki, Ois Franç, Nikolai Nadirashvili. 2010

245 citations recorded by the source corpus.

A modular ramp system includes a ramp component and a connector releasably joined to the ramp component. The ramp component has first and second inclined surfaces and a connecting portion positioned between the first and second inclined surfaces. The connector has a bottom side formed with first and second coupling sections connectible to the connecting portion. The connector is positionable in a first position in which one of the first and second coupling sections is releasably joined to the connecting portion of the ramp component, and the other of the first and second coupling sections is adapted to releasably couple to a ramp or an external structure, and is positionable in a second position in which the first and second coupling sections are releasably joined to the connecting portion of the ramp component.

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

View Paper: https://www.semanticscholar.org/paper/4b21f4dceec6edd21bfe3a8f96b27b47c78289d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Numerical Analysis

In Public Health, Environmental and Occupational Health

Citations in the corpus

Propagation dynamics for monotone evolution systems without spatial translation invariance (2020, background): “[5, 6] studied the asymptotic spreading speed for KPP equations in periodic or non-periodic spatial domains.”
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.”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, unknown): “24) where f(t, x, u) < 0 for u ≫ 1, ∂uf(t, x, u) < 0 for u ≥ 0 (see [3, 4, 5, 6, 10, 11, 25, 26, 27, 29, 30, 33, 34, 41, 42, 53], etc.”
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary (2010, unknown): “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; we refer to [30, 13, 28, 3, 4, 17, 29] and the references therein for more details.”
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] ”
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations (2011, unknown): “Put c∗ = 2. c∗ is of the following spatially spreading property: for any nonnegative solution u(t, x) of (1.2), if at time t = 0, u(0, x) ≥ σ for some σ > 0 and x ¿ −1 and u(0, x) = 0 for x À 1, then inf x≤c′ t |u(t, x)− 1| → 0, ∀c′ < c∗ and sup x≥c′′ t u(t, x) → 0 ∀c′′ > c∗ as t →∞.”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, background): “Berestycki, Hamel and Nadirashvili [4, 6] investigated spreading properties in higher dimension for the homogeneous equation in general unbounded domains such as spirals, infinite combs or cusps, with Neumann boundary conditions.”
Generalized Transition Waves and Their Properties (2010, unknown): “We also refer to [7] for further definitions and properties of the spreading speeds of the solutions of the Cauchy problem ut = ∆u+f(u) with compactly supported initial conditions, in arbitrary domains Ω and no-flux boundary conditions.”
Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity (2008, methodology): “19), is positive, see [5] (actually, this existence result has been proved under additional smoothness assumptions on the coefficients of (1.”
Bistable Traveling Waves for Monotone Semiflows with Applications (2011, background): “For monostable systems in periodic habitats, we refer to [5, 8, 9, 22, 23, 26] and references therein.”