Global Classical Solutions for the Initial Boundary Value Problems in Variable Nozzle Flows

李信儀 博士

國立中央大學數學系

Department of Mathematics, National Central University

Abstract

    In this talk, we study the global existence of classical solutions for the initial boundary value problem of the isentropic supersonic flows near vacuum through ducts expanding with space and time. The global existence of classical solutions has been investigated for decades by many researchers who focus on nonlinear hyperbolic dissipative or relaxation systems under the assumptions of small data in the -norm or -norm sense. In our work, the governing equations are the compressible Euler equations with a sufficiently small variable parameter, which can be written as a hyperbolic system in terms of the Riemann invariants with a non-dissipative source. We prove a couple of global existence theorems of classical solutions for non-dissipative hyperbolic balance laws under the suitable conditions of expanding ducts and the initial-boundary data whose-norms can be large. Our work is based on the local existence theorem and the uniform a priori estimates obtained by giving the maximum principle and introducing new generalized Lax transformations. The asymptotic behavior of global classical solutions is shown via the behavior of Riemann invariants along each characteristic curve and vertical line. We also study the feasibility of the initial value problem for such expanding ducts.

日  期:111年2月23日(星期三) 16:10~17:00

地  點：本校數學館527教室（嘉義縣民雄鄉大學路168號）

茶  會：15:30~16:00數學館四樓409室舉行

歡迎參加   敬請公佈