|場所：||京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟） 3階 b3n03室（航空宇宙工学専攻会議室）|
|講演1：||PDE-based modelling of biological network formation|
|Dr. Jan Haskovec (Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Kingdom of Saudi Arabia)|
|要旨1：||Motivated by recent papers describing rules for natural network formation in discrete settings, we propose an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to Darcy’s type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We show that patterns (network structures) occur in the regime of small material randomness. Moreover, we present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions.|
|講演2：||Transport phenomena in evolutionary domains|
|Prof. Francesco Salvarani
(CEREMADE – Université Paris-Dauphine, France & Dipartimento di Matematica, Università di Pavia, Italy)
|要旨2：|| We study the transport equation in a time-dependent vessel with absorbing boundary, in any space dimension. We first prove existence and uniqueness, and subsequently we consider the problem of the time-asymptotic convergence to equilibrium. We show that the convergence towards equilibrium heavily depends on the initial data and on the evolution law of the vessel.
Subsequently, we describe a numerical strategy to simulate the problem, based on a particle method implemented on general-purpose graphics processing units (GPGPU). We observe that the parallelization procedure on GPGPU allows for a marked improvement of the performances when compared with the standard approach on CPU.