Homogenization of a Convection–Diffusion Equation in a Thin Rod Structure
This chapter is devoted to the homogenization of a stationary convection diffusion model problem in a thin rod structure. More precisely, we study the asymptotic behavior of solutions to a boundary value problem for a convection diffusion equation defined in a thin cylinder that is the union of two nonintersecting cylinders with a junction at the origin. We suppose that in each of these cylinders the coefficients are rapidly oscillating functions that are periodic in the axial direction, and that the microstructure period is of the same order as the cylinder diameter. On the lateral boundary of the cylinder we assume the Neumann boundary condition, while at the cylinder bases the Dirichlet boundary conditions are posed.
KeywordsStationary Convection Thin Cylinder Microstructure Period Boundary Layer Function Linearize Elasticity System
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