Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109200

Title:	Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section
Authors:	洪盟凱;Hong, John M.;Hsu, Cheng-Hsiung;Huang, Bo-Chih
Contributors:	理學院數學系
Keywords:	Compressible Euler equations;Discontinuous nozzle;Enthalpy;Entropy condition;Geometric singular perturbations;Hellyʼs selection principle;Transonic steady-states;Viscous conservation laws
Date:	2012-08-15
Issue Date:	2026-04-23 16:14:58 (UTC+8)
Publisher:	Academic Press Inc.;Elsevier Inc
Abstract:	摘要： In this paper we study the existence and uniqueness of the generalized stationary waves for one-dimensional viscous isentropic compressible flows through a nozzle with discontinuous cross section. Following the geometric singular perturbation technique, we establish the existence and uniqueness of inviscid and viscous stationary waves for the regularized systems with mollified cross section. Then, the generalized inviscid stationary waves are classified for discontinuous and expanding or contracting nozzles by the limiting argument. Moreover, we obtain the generalized viscous stationary waves by using Hellyʼs selection principle. However, due to the choices of mollified cross section functions, there may exist multiple transonic standing shocks in the generalized stationary waves. A new entropy condition is imposed to select a unique admissible standing shock in generalized stationary wave. We show that, such admissible solution selected by the entropy condition, admits minimal total variation and has minimal enthalpy loss across the standing shock in the limiting process. 出版者： Elsevier Inc 出版日期： 2012-08-15 出處： Journal of Differential Equations, 2012-08, Vol.253 (4), p.1088-1110 資源來源： Elsevier ScienceDirect Journals 版權： 2012 Elsevier Inc. 識別號： ISSN: 0022-0396 識別號： EISSN: 1090-2732 識別號： DOI: 10.1016/j.jde.2012.04.021
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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