Top PDF Fast propagation in reaction-diffusion equations with fractional diffusion
Fast propagation in reaction-diffusion equations with fractional diffusion
... problems. In Chapter 1, we have applied our method on a Fisher-KPP model in periodic media with fractional ...exponentially fast in time, and we have obtained the precise ...
176
Propagation acceleration in reaction diffusion equations with anomalous diffusions
... argument in Section 3. Acknowledgement. J.Coville carried out this work in the framework of Archim`ede Labex (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the ...
31
Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity
... a reaction-diffusion equation is often used in ecology and population dynamics to model spatial propagation phenomena [ 1 ...]. In this context, the unknown function u denotes the ...
35
A singular limit in a fractional reaction-diffusion equation with periodic coefficients
... that in the fractional case, the speed of propagation does not depend anymore on the ...of propagation is exponential in time with a precise exponent depending on a periodic ...
24
Persistence and propagation in periodic reaction-diffusion models
... . In the moving frame with speed c to the right, a traveling front u(t, x) = φ(x − ct) is invariant in ...stable with respect to some natural classes of perturbations, see ...heterogeneous ...
13
Two examples of reaction-diffusion front propagation in heterogeneous media
... for reaction-diffusion equations have been studied since the well known works of Kolmogorov, Petrovskii and Piskunov ...generalised in the late seventies by Aronson and Weinberger [2] and Fife ...
140
Transition fronts for periodic bistable reaction-diffusion equations
... for diffusion and reaction coefficients a(x) and f (x, u) satisfying ...of propagation speeds are still open, even under the additional assumption ...work in this present paper and the ...
37
A variational approach to reaction diffusion equations with forced speed in dimension 1
... change Reaction diffusion problems are often used to model the evolution of biological ...species. In 1937, Kolmogorov, Petrovskii and Piskunov in [15], Fisher in [10] used ...
35
Reaction diffusion equation in heterogeneous media : persistance, propagation and effect of the geometry
... fronts in non homogeneous ...heterogeneous with respect to time in the bistable, monostable and KPP ...bistable reaction diffusion ...heterogeneities. In all these papers it has ...
217
Periodic Homogenization for Weakly Elliptic Hamilton-Jacobi-Bellman Equations with Critical Fractional Diffusion
... is in striking contrast with previous available results in homogenization of integro-differential ...problems. In [2, 3], Arisawa analyzed periodic homogenization for equa- tions with ...
36
Spreading speeds for one-dimensional monostable reaction-diffusion equations
... (φ(x)), with µ 0 a periodic function and φ a smooth increasing function such that φ ′ (x) → 0 as x → ...sufficiently fast, then these authors proved that w ∗ = w ∗∗ and it is possible to compute this ...
31
Critical travelling waves for general heterogeneous one-dimensional reaction-diffusion equations
... translation in time, such as ignition-type or monostable equations, these waves satisfy a property which is close to the translation property introduced in [18] (Proposition ...waves in the ...
49
Accélération de la propagation dans les équations de réaction-diffusion par une ligne de diffusion rapide
... fronts, propagation, ...of propagation in reaction- diffusion equations, through a new mechanism involving a line with fast ...coupling with strong ...
146
Propagation phenomena and reaction–diffusion systems for population dynamics in homogeneous or periodic media
... systems with periodic diffusion and interspecific competition rates, an existence result is ...stick with the aforementioned ...scalar reaction–diffusion equations in ...
328
Diameters of the level sets for reaction-diffusion equations in nonperiodic slowly varying media *
... consists in showing that the solution u of (1.1) and (1.5) with this function f satisfies the desired conclusions listed in Theorem ...the propagation in some time intervals when the ...
16
Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat
... given in [25, 28, ...fronts In this paper, we first discuss the question of the uniqueness of the speed of pulsating fronts for the bistable equation ...fronts with nonzero speed. In [9], ...
58
Propagation phenomena for time heterogeneous KPP reaction–diffusion equations
... depends in a general way on t ∈ ...u), with µ ∈ L ∞ (R) such that ess inf t∈R µ(t) > ...defined in [4, 22]) for a given class of ...function with respect to t ∈ ...
27
Fractional reaction-diffusion problems
... established in Chapter 1. Additionally we recall the earlier work in the case α ∈ (0, 1) by Berestycki, Roquejoffre and Rossi [10], where it is proved that there is invasion of the unstable state by the ...
98
Langevin equations for reaction-diffusion processes
... For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically-tractable, exact Langevin equations that govern a stochastic variable related to the ...
12
Phase portrait control for 1D monostable and bistable reaction-diffusion equations
... waves in the form y(x − ct) for certain speeds c, linking the states 0 and 1, see the pioneering work [ 10 ...fulfilled with non-negative Dirichlet boundary ...
31