Asymptotic modelling of a dynamic response of multiscale systems

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We consider the asymptotic analysis of singularly perturbed problems for partial differential equations and its applications in propagation of waves, heat conduction and mathematical elasticity. We also study the asymptotic analysis of fields in multi-structures and the asymptotic behaviour of solutions to boundary value problems. For networks of fluids in thin channels, asymptotic approximations will be constructed with the focus on the analysis of junctions of the network, and both slow flows and dynamic regimes will be addressed. Furthermore, the formulations, which take into account the fluid-solid interaction, will include the wave phenomena. Such waves are dispersive, and their dynamics in multi-scale networks is a challenge. Analytical models will be accompanied by numerical simulations. Applications are envisaged in the analysis of vascular systems in biological systems as well as rock dynamics in the studies of earthquake phenomena.