Boundary-layer and shock-layer solutions to singularly perturbed boundary-value problems

Thesis/Dissertation · Thu Jan 01 00:00:00 EST 1987

OSTI ID:7108990

Jeffries, J S

This dissertation concerns the study of certain singularly perturbed boundary value problems. In the first part of this dissertation (Chapters 2 and 3), a singularly perturbed nonlinear system of differential equations are considered over a compact interval, subject to general boundary conditions that allow the coupling of the boundary values at the different endpoints. It is shown, subject to suitable conditions, that there exists solutions of boundary-layer type, i.e., solutions that experience a rapid variation at one or both endpoints. In the second part (Chapter 4), a singularly perturbed second-order scalar differential equation is considered over a compact interval subject to Dirichlet boundary conditions. Subject to suitable conditions, there exist solutions of shock-layer type, i.e., solutions that experience a rapid transition at an interior point. For both the singularly perturbed system and the second-order scalar equation, a proposed approximate solution is constructed using the O'Malley construction, and a Riccati transformation is then used in a direct construction of the Green function for linearization of the problem about the proposed approximate solution.

• Research Organization: California Univ., San Diego (USA)
• OSTI ID: 7108990
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
BOUNDARY-VALUE PROBLEMS
NONLINEAR PROBLEMS
BOUNDARY LAYERS
DIRICHLET PROBLEM
GREEN FUNCTION
RICCATI EQUATION
SHOCK WAVES
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
LAYERS
657000* - Theoretical & Mathematical Physics
420400 - Engineering- Heat Transfer & Fluid Flow