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The Motion of Internal Layers in Singularly Perturbed Advection‐Diffusion‐Reaction Equations *
Author(s) -
Knaub Karl R.,
O'Malley Robert E.
Publication year - 2004
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 - 10.1111/j.1467-9590.2004.01502.x
Subject(s) - advection , mathematics , mathematical analysis , domain (mathematical analysis) , algebraic number , exponential function , partial differential equation , motion (physics) , algebraic equation , method of matched asymptotic expansions , singular perturbation , reaction–diffusion system , diffusion , differential equation , physics , classical mechanics , nonlinear system , quantum mechanics , thermodynamics
This paper asymptotically solves singularly perturbed partial differential equations of the formas ε→ 0 + , on a finite spatial domain, in the case where the solution exhibits a single extremely slowly moving internal layer. Conditions under which such solutions occur are discussed. Equations of motion for the layer are derived, and careful consideration is given to both exponential asymptotics and the previously little‐studied case of algebraic asymptotics.