| Abstract: |
| In the last years, the improvements of industrial techniques has permitted to obtain more efficient materials constructed by assembling different constituents, whose physical properties are definitely superior than the ones of the single components.
However, this bonding does not give rise in general to perfect contacts between the different components, so that discontinuities in the involved physical fields can appear.
Also the study of boundary value problems in composites with rough boundaries or interfaces is a topic that has recently attracted a significant interest due to their applications in many areas of natural or engineering sciences, such as fluid mechanics, materials science, biology, etc.
In this talk, we present some recent results concerning the study of problems where imperfect contact conditions couple with oscillating interfaces.
More precisely, we consider a stationary heat diffusion problem in a two-component material, which exhibits an
imperfect contact across an oscillating interface separating the two constituents. At the microscopic scale,
it is mathematically described by an elliptic boundary value problem stated in each of two connected components. The heat potential is continuous across the interface, while its flux jumps according to suitable prescribed conditions, which lead to different macroscopic models, obtained through an asymptotic analysis. |
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