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Some Stability Results for Advection‐Diffusion Equations
Author(s) -
Howes F. A.
Publication year - 1986
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198674135
Subject(s) - advection , mathematics , transonic , perturbation (astronomy) , boundary layer , mechanics , mathematical analysis , stability (learning theory) , steady state (chemistry) , physics , thermodynamics , aerodynamics , computer science , chemistry , quantum mechanics , machine learning
The stability of steady‐state solutions of reaction‐advection‐diffusion equations to perturbations in the initial data is examined by means of a comparison theorem. In particular, conditions on the reactive terms and the advective terms are used to prove stability or asymptotic stability of steady boundary‐layer and shock‐layer solutions and to estimate the maximum allowable size of the initial perturbation. Many examples are discussed, including the time‐dependent Lagerstrom‐Cole problem and a problem modeling transonic flow in a nonuniform duct.