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TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC boundary CONDITIONS

Acta Mathematica Scientia 2019年第2期39卷 403-412页

作者：袁海荣 School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal University

We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.

关键词： supersonic flow isentropic compressible Euler equations duct time-periodic solution initial-boundary-value problem

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Unconventional Hamilton-type variational principles for electromagnetic elastodynamics

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Science China(Physics,Mechanics & Astronomy) 2006年第1期49卷 119-128页

作者： LUO En ZHU Huijian YUAN Lei Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.

关键词： electromagnetic elastodynamics, unconventional Hamilton-type variational principle, principle of virtual work, dual-complementarity, initial-boundary-value problem.

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CONVERGENCE OF DIFFERENCE METHODS FOR NONLINEAR PROBLEMS WITH MOVING BOUNDARIES

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Science China Mathematics 1990年第5期33卷 537-550页

作者：雍稳安朱幼兰 Computing Center Academia Sinica Beijing 100080 PRC

In this paper, we discuss convergence of difference methods for initial-boundary-value problems of quasilinear hyperbolic systems with moving boundaries in two independent variables, where the differences across the boundaries do not appear and the boundary conditions are nonlinear. Such a class of problems come from the "singularity-separating difference method" for initial-boundary-value problems of quasilinear hyperbolic systems.

关键词： difference methods initial-boundary-value problems quasilinear-hy-perbolic systems.

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