Asymptotic modelling of a dynamic response of multiscale systems

讨论了偏微分方程奇异摄动问题的渐近分析及其在波传播、热传导和数学弹性中的应用。我们还研究了多结构域的渐近分析和边值问题解的渐近性质。对于薄通道中的流体网络，将构建渐近逼近，重点分析网络的连接点，并讨论慢流和动态状态。此外，考虑流固相互作用的公式将包括波动现象。这种波是分散的，在多尺度网络中它们的动力学是一个挑战。分析模型将伴随着数值模拟。预计应用于生物系统中的维管系统分析以及地震现象研究中的岩石动力学。

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.