... integro-differential **reaction**-**diffusion** equations from simple ...the **fractional** **diffusion** type, they also prove the convergence of solutions of **fractional** evolution problem to the ...

98

... We propose and study a posteriori error estimates for convection–**diffusion**–**reaction** prob- lems with inhomogeneous and anisotropic **diffusion** approximated by weighted interior- penalty discontinuous ...

27

... Part I of the thesis has been devoted to a rigorous analysis of the asymptotic location of the level sets of the solution to two different **problems**. In Chapter 1, we have applied our method on a Fisher-KPP model ...

176

... convective-dominated **problems** and **problems** in which the singular behavior comes from a large undifferentiated term compared with the second-order ...

25

... non-Gaussian **diffusion** is still topical in many different fields such as statistical physics, condensed matter physics or biology – as testified by the present special issue of ...of **fractional** ...

8

... for **reaction**-**diffusion** **problems** that enables interaction with the simulation during the execution, and we establish a mathematical validation for our ...a **reaction**-agent rep- resents an ...

10

... the **reaction** part of the ...scalar **reaction**-diﬀusion equations, and then illustrate on a few particular examples how the general idea can be adapted to treat ...

27

... the **fractional** Laplacian and a constant environment, Cabré and Roquejoffre in [8] proved the front position is exponential in time (see also for instance [11] for some heuristic and numerical works predicting such ...

24

... [25] S. Heinze, Large convection limits for KPP fronts, preprint. [26] J. Huang, W. Shen, Speeds of spread and propagation for KPP models in time almost and space periodic media, SIAM J. Appl. Dyn. Syst. 8 (2009), ...

13

... 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 response field ...

12

... Remark 3 The result obtained in Theorem 3.2 can be of course generalizes in the case when the generator L is just an operator satisfying a spectral gap inequality on the domain considered Ω. For example one can consider ...

20

... the **reaction**-**diffusion** model can be replaced by other types of models such as individual based models (Gross et ...the **reaction**-**diffusion** approach was encouraged by computational speed ...

18

... Motivations **Reaction**-**diffusion** equations have drawn a lot of attention from the mathematical community over the last decades, but most usually in spatially homogeneous setting, while the lit- erature ...

265

... Our goal in this paper is to state similar results for coupled parabolic systems of the form ( 1.1 ) with internal control. This framework raises several difficulties. Indeed, for boundary control or equations satisfying ...

21

... ∂ t q + v∇ x q + ∂ y (f (y, S)q) = Λ(y, S)(hqi − q) . (0.1) Here q(t, x, v, y) denotes the probability density function of bacteria at time t, position x ∈ R d , velocity v ∈ V with V the sphere (or the ball) with radius ...

12

... boundary **problems** associated with space-**fractional** ...turns **problems** whose well-posedness is not assessed: solutions do exist but uniqueness apparently depends on how we interpret these boundary ...

24

... homogenization **problems** and spreading properties for **reaction**-**diffusion** ...homogenization **problems** and on the existence of approximate correctors, a notion which is close to that of ...

31

... monostable type of nonlinearity, see for example [2, 25, 31, 33]. On the other hand, thanks to the work of Fife and Mc Leod [17], and Alfaro [2] we can see that accelerated transitions will never occur when the ...

31

... the **reaction** and for so- lutions emanating from initial conditions with general unbounded support, whereas most of earlier results were concerned with more specific reactions and compactly supported or ...

89

... 5. K. Diethelm and A. D. Freed, On the solution of nonlinear **fractional** order differen- tial equations used in the modeling of viscoplasticity. In: Scientific Computing in Chem- ical Engineering II-Computational ...

12