日本航空宇宙学会関西支部分科会「流体力学における現代的アプローチ」講演会

Boundary Kernel for Dissipative Systems

Part I

Dissipative Wave Equations
(Prof. Tai-Ping Liu, Academia Sinica, Taiwan & Stanford University, USA)

Part II

Compressible Navier-Stokes Equations
(Prof. Shih-Hsien Yu, National University of Singapore, Singapore)

要旨

We will present a systematic approach to the study of the kernel for the boundary Dirichlet-Neumann relations for dissipative partial differential equations. Our study exhibits interesting relation between the wave propagation along the boundary and the differentiation normal to the boundary. The key notions of Laplace-Fourier Path and Boundary Determinant will be illustrated for the dissipative wave equations and the compressible Navier-Stokes equations. Our approach involves interesting algebraic calculations for the transformed variables and the inversion of the Fourier and Laplace transforms by the subtle complex analytic techniques.