Now showing items 1-10 of 10
Periodic homogenization of nonlocal operators with a convolution-type kernel
(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
The paper deals with a homogenization problem for a nonlocal linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diﬀusive scaling of this operator and study the limit behavior of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators ...
Resolvent bounds for jump generators
(Journal article; Peer reviewed; Tidsskriftartikkel, 2016-12-02)
The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise ...
Homogenization of Levy-type operators with oscillating coefficients
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019-01-05)
The paper deals with homogenization of Lévy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Lévy-operator. In the periodic case we study both symmetric and non-symmetric kernels whereas in the random case we only investigate symmetric kernels. We also address a nonlinear ...
Asymptotics of fundamental solutions for time fractional equations with convolution kernels
(Journal article; Peer reviewed, 2020-09-11)
The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation with a convolution type operator. In this equation we use a Caputo time derivative of order α ∈ (0, 1), and assume that the convolution kernel of the spatial operator is symmetric, integrable and shows a super-exponential decay at infinity. Under these assumptions we describe the ...
Pointwise estimates for heat kernels of convolution-type operators
(Journal article; Peer reviewed; Tidsskriftartikkel, 2018-04-16)
We study the large‐time behaviour of the fundamental solution of parabolic equations with an elliptic part being non‐local convolution‐type operator. We assume that this operator is a generator of a Markov jump process, and that its convolution kernel decays at least exponentially at infinity. The fundamental solution shows rather different asymptotic behaviour depending on whether | x | ≲ t , or t ...
Limit behaviour of diffusion in high-contrast periodic media and related Markov semigroups
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
The goal of the paper is to describe the large time behaviour of a symmetric diffusion in a high-contrast periodic environment and to characterize the limit process under the diffusive scaling. We consider separately the C0 and the L2 settings.
Homogenization of biased convolution type operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019-11-07)
This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We determine the corresponding effective velocity and prove that the limit operator is a second order parabolic operator with constant coefficients. We also consider ...
Large deviations for Markov jump processes in periodic and locally periodic environments
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-12)
The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating locally periodic coefficient and, under natural ellipticity and localization conditions, show that the family satisfies the large deviation principle in the path space ...
On operator estimates in homogenization of nonlocal operators of convolution type
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-01-11)
Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media<sup>∗</sup>
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-23)
The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scaling is diffusive that is the scaling factor of the temporal variable is equal to the square of ...