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Some Stability Results for Advection‐Diffusion Equations. II
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/sapm1986752153
Subject(s) - advection , conservation law , shock (circulatory) , perturbation (astronomy) , dissipation , mathematics , scalar (mathematics) , mechanics , mathematical analysis , convection–diffusion equation , classical mechanics , physics , thermodynamics , geometry , medicine , quantum mechanics
Previous results on the stability of steady shock layer solutions of scalar reaction‐advection‐diffusion equations are strengthened by means of a more detailed treatment of the perturbation inside the shock. These sharper results verify a recent conjecture of Embid, Goodman, and Majda on the asymptotic stability of a standing shock in a diverging duct, and they suggest that a study of analogous questions for systems of conservation laws with dissipation is possible.