アイントホーフェン工科大学講義　（Rafael Bailo先生１）

• アイントホーフェン工科大学

金沢大学にて2026年3月に実施した特別講義です。
講師：
Rafael Bailo氏（オランダ・アイントホーフェン工科大学）
Title:
The Aggregation-Diffusion Equation
Abstract:
　Aggregation–diffusion equations are a prototypical class of non-linear PDEs describing the competition between attractive interactions and diffusive effects. They arise in models of collective behaviour, granular media, biological swarms, and self-organising systems. In this talk, I will introduce the aggregation–diffusion equation, explain the role of the interaction kernel and the diffusion term, and discuss the main qualitative behaviours of solutions, including concentration, pattern formation, and steady states.
　Starting from interacting particle systems, I will show how these equations can be derived through mean-field limits, highlighting the link between microscopic dynamics and macroscopic PDEs. I will then present the Wasserstein gradient-flow structure of the equations, which provides a unifying variational framework for well-posedness, long-time behaviour, and stability. Finally, I will discuss structure-preserving numerical methods inspired by this gradient-flow formulation, focusing on finite-volume and particle schemes that respect key properties such as positivity, mass conservation, and energy dissipation.

本講義は、令和6年度文部科学省　大学の世界展開力強化事業～EU諸国等との大学間交流形成支援～の交流プログラムの一環として実施したものです。
https://eutenkai.w3.kanazawa-u.ac.jp/