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Now showing items 1-10 of 19

#### 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 ...

#### Stationary convection-diffusion equation in an infinite cylinder

(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12-21)

We study the existence and uniqueness of a solution to a linear stationary convection–diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of two semi-infinite cylinders with two different periodic regimes. Depending on the direction of the effective convection in the two semi-infinite cylinders, we ...

#### Homogenization of biomechanical models for plant tissues

(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)

In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical ...

#### Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media

(Journal article; Peer reviewed, 2018-03-15)

In this paper, we consider nonisothermal two-phase flows through heterogeneous porous media with periodic microstructure. Examples of such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste, thermally enhanced oil recovery and geothermal systems. The mathematical model is given by a coupled system of two-phase flow equations, and an ...

#### 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 ...

#### Topological Singularities in Periodic Media: Ginzburg–Landau and Core-Radius Approaches

(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-12-20)

We describe the emergence of topological singularities in periodic media within
the Ginzburg–Landau model and the core-radius approach. The energy functionals
of both models are denoted by Eε,δ, where ε represent the coherence length (in the
Ginzburg–Landau model) or the core-radius size (in the core-radius approach) and
δ denotes the periodicity scale. We carry out the -convergence analysis ...

#### 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 ...

#### Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime

(Journal article; Peer reviewed, 2018-04-30)

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability
1−p
1−p
and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in
Z
2
Z2
. We prove that there exists
p
0
p0
such that for
p≤
p
0
p≤p0
such ...