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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 ...