Thermal Vibrations and Localisation Phenomena for Solids with Singularly Perturbed Boundaries

We plan to study solutions of problems of thermoelasticity in singularly perturbed domains that include subsets of different limit dimensions (multi-structures). A particular feature of the asymptotic approximations used here is the dependence on fast (scaled) variables and hence the presence of boundary layers in the vicinity of singularly perturbed boundaries (e.g. neighbourhoods of junctions regions between elements of a multi-structure). Model fields of the boundary layer type will be studied numerically, and for a certain class of boundary layer formulations analytical solutions are also feasible (for example, some of our model problems can be reduced to functional equations of the Wiener Hopf type). We also plan to use an asymptotic method involving the analysis of Floquet waves in periodic thermoelastic structures to study the influence of a thermal load on transmission and reflection properties of highly porous slabs.