... 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

... 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

... 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

... 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

... . **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

... 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

... 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

... 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

... 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

... 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

... (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

... 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

... fronts, **propagation**, ...of **propagation** **in** **reaction**- **diffusion** **equations**, through a new mechanism involving a line **with** **fast** ...coupling **with** strong ...

146

... systems **with** periodic **diffusion** and interspecific competition rates, an existence result is ...stick **with** the aforementioned ...scalar **reaction**–**diffusion** **equations** **in** ...

328

... 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

... 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

... 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

... 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

... 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

... 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