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Dyadic nonlocal diffusion in metric measure spaces
(De Gruyter, 2015-06)
In this paper we solve the initial value problem for the nonlocal diffusion generated by the space fractional derivative induced by the dyadic tilings of M. Christ on a space of homogeneous type. We consider the problems ...
Boundary fluxes for nonlocal diffusion
(Academic Press Inc Elsevier Science, 2007-12)
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove ...
Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
(Springer, 2012-08)
The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, ut = J ∗u −u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on RN \Ω. When ...
RANDOM WALKS AND THE POROUS MEDIUM EQUATION
(UNION MATEMATICA ARGENTINA, 2009)
In this paper we consider a fixed initial condition u(0) and we study the limit as epsilon -> 0 of u(epsilon), the solution to the re-scaled problem
Quenching for Discretizations of a Nonlocal Parabolic Problem with Neumann Boundary Condition
(Universidad de La Frontera. Departamento de Matemática y EstadísticaUniversidade Federal de Pernambuco. Departamento de Matemática, 2010)
A nonlocal diffusion problem with a sharp free boundary
(European Mathematical Society, 2019-12)
We introduce and analyze a nonlocal free boundary problem which may be of interest to describe the spreading of populations in hostile environments. The rate of growth of the volume of the region occupied by the population ...
Pointwise convergence to the initial data for nonlocal dyadic diffusions
(Springer Heidelberg, 2016-03)
In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar ...
Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations
(Discrete and Continuous Dynamical Systems, 2020)
Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations
(Discrete and Continuous Dynamical Systems, 2020)
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SOME INHOMOGENEOUS NONLOCAL DIFFUSION PROBLEMS
(SIAM PUBLICATIONS, 2009)
We consider the nonlocal evolution Dirichlet problem u(t)(x, t) = f(Omega) J(x-y/g(y)) u(y, t)/g(y)(N) dy- u(x, t), x is an element of Omega, t > 0; u = 0, x is an element of R-N\Omega, t >= 0; u(x, 0) = u(0)(x), x is an ...