Nonlinear Singular Sturm-Liouville Problems and an Application to Transonic Flow through a Nozzle

Abstract

Consider a class of singular Sturm-Liouville problems with a nonlinear convection and a strongly coupling source. The investigation is motivated by, and then applied to, the study of transonic gas flow through a nozzle. Interested exists in such solution properties as the exact number of solution, 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 this 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. Reprints.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA217394

Entities

People

  • Sze-bi Hsu
  • Tai-ping Liu

Organizations

  • New York University

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Asymptotic Series
  • Boundaries
  • Boundary Layer
  • Equations
  • Flow
  • Gas Flow
  • Layers
  • Mathematics
  • Rarefaction
  • Shock
  • Shock Waves
  • Stationary
  • Steady State
  • Transonic Flow
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)