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今後の応用解析研究会(2022年度)

講演者: Jack Xin（UC Irvine）
講演題目: Particle and Game Theoretic Methods for Front Speeds in Fluid Flows
アブストラクト: We study and compute large time front speeds of Fisher-Kolmogorov-Petrovsky-Piskunov equation in fluid flows with chaotic and stochastic streamlines based on a normalized Feynman-Kac representation and the associated genetic interacting particle (IP) method. Examples of such flows are Arnold-Beltrami-Childress (ABC) flows and their random perturbations. The method is mesh-free and self-adaptive, providing training data for efficient deep learning of the invariant measure of IP evolution in the small molecular diffusivity regime.

We analyze a curvature dependent level set Hamilton-Jacobi equation arising in turbulent combustion, and show the existence of effective front speeds in cellular (BC) flow. To overcome non-coercivity and non-convexity of the Hamiltonian, we leverage Kohn-Serfaty deterministic game characterization and streamline structure of the cellular flow.
場所: 早稲田大学西早稲田キャンパス 55 号館 N棟 1階第 2 会議室

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