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Irina Pettersson (UiT Narvik) - “Existence and uniqueness results for a stationary convection-diffusion equation in cylindrical domains” - joint work with A. Piatnitski
We study the existence and uniqueness of a bounded solution to a stationary convection-diffusion equation in semi-infinite and infinite cylindrical domains. The operator is not self-adjoint, and depending on the direction of the effective convection we either get a unique solution, a family of solutions or even non-existence.
Klas Pettersson (UiT Narvik) - “Elasticity, shape and size of a planar perforated structure”
We present a relation between local and effective properties for a planar two-dimensional elastic structure. The model considered is a periodic structure that is locally isotropic and homogeneous. The corresponding physical model is a flat two-dimensional body with traction-free holes, such as a perforated plate. We show how the effective properties of the structure depend on the local properties in a way that separates the dependence on the shape and size of the holes.