Asymptotic analysis of a singular perturbation problem
In a rectangle 0 less than or equal to x less than or equal to a and 0 less than or equal to y less than or equal to b, the Dirichlet problem is studied for an elliptic differential equation of the form -epsilon ..delta..u/sub epsilon/ + p (delta/delta x)u/sub epsilon/ + pu/sub epsilon/ = f(x,y) were epsilon is a small parameter 0 < epsilon << 1, ..delta.. is the Laplace operator, p is a positive number, p is a nonnegative number, and all of the input data are smooth. A constructive procedure is established for obtaining an asymptotic approximation of arbitrary order with respect to epsilon of this singular perturbation problem, and also, a proof is given of its uniform validity in the closed rectangle by use of the maximum principle and exponential estimates of all boundary or corner layer functions. The corner singularities of parabolic boundary layer functions are removed by introducing elliptic boundary layers along the characteristic boundaries y = 0 and y = b. Both ordinary corner layers and elliptic corner layers are employed at the outflow corners (a,0) and (a,b). An application is made to settle a long-standing problem in the magnetohydrodynamic flow in a rectangular duct.
- Research Organization:
- Maryland Univ., College Park (USA)
- OSTI ID:
- 5264137
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MHD CHANNELS
FLUID FLOW
PERTURBATION THEORY
RECTANGULAR CONFIGURATION
DIRICHLET PROBLEM
ASYMPTOTIC SOLUTIONS
BOUNDARY LAYERS
DUCTS
CONFIGURATION
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640430* - Fluid Physics- Magnetohydrodynamics
658000 - Mathematical Physics- (-1987)