Gradient estimates and symmetrization for Fisher–KPP front propagation with fractional diffusion
نویسندگان
چکیده
منابع مشابه
Front propagation in hyperbolic fractional reaction-diffusion equations.
From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition...
متن کاملFront propagation and critical gradient transport models
This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear resp...
متن کاملDirichlet Heat Kernel Estimates for Fractional Laplacian with Gradient Perturbation
By Zhen-Qing Chen∗,‡, Panki Kim†,§ and Renming Song¶ University of Washington‡, Seoul National University§ and University of Illinois¶ Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C open set in R and b an R-valued function on R whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for ...
متن کاملHybrid method for simulating front propagation in reaction-diffusion systems.
We study the propagation of pulled fronts in the A<--> A+A microscopic reaction-diffusion process using Monte Carlo simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov equation. In particular, we concentrate on the corrections to the deterministic behavior due to the number of particles per correlated volume Omega. By ...
متن کاملSharp Energy Estimates for Nonlinear Fractional Diffusion Equations
We study the nonlinear fractional equation (−∆)u = f(u) in R, for all fractions 0 < s < 1 and all nonlinearities f . For every fractional power s ∈ (0, 1), we obtain sharp energy estimates for bounded global minimizers and for bounded monotone solutions. They are sharp since they are optimal for solutions depending only on one Euclidian variable. As a consequence, we deduce the one-dimensional ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2017
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2017.07.001