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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 ...
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.
Singularly perturbed spectral problems in a thin cylinder with fourier conditions on its bases
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
The paper deals with the bottom of the spectrum of a singularly perturbed second order elliptic operator defined in a thin cylinder and having locally periodic coefficients in the longitudinal direction. We impose a homogeneous Neumann boundary condition on the lateral surface of the cylinder and a generic homogeneous Fourier condition at its bases. We then show that the asymptotic behavior of the ...
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 ...