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Nonlinear singular sturm‐liouville problems and an application to transonic flow through a nozzle
Author(s) -
Hsu SzeBi,
Liu TaiPing
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430103
Subject(s) - transonic , mathematics , uniqueness , nonlinear system , flow (mathematics) , mathematical analysis , boundary (topology) , a priori and a posteriori , singular solution , nozzle , boundary value problem , mechanics , geometry , aerodynamics , physics , thermodynamics , philosophy , epistemology , quantum mechanics
We consider a class of singular Sturm‐Liouville problems with a nonlinear convection and a strongly coupling source. Our investigation is motivated by, and then applied to, the study of transonic gas flow through a nozzle. We are interested in such solution properties as the exact number of solutions, the location and shape of boundary and interior layers, and nonlinear stability and instability of solutions when regarded as stationary solutions of the corresponding convective reaction‐diffusion equations. Novel elements in our theory include a priori estimate for qualitative behavior of general solutions, a new class of boundary layers for expansion waves, and a local uniqueness analysis for transonic solutions with interior and boundary layers.