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Transient Solutions to Some Weakly Diffusive Nonlinear Diffusion Equations
Author(s) -
Lange C. G.,
Larson D. A.
Publication year - 1980
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/sapm1980633249
Subject(s) - transient (computer programming) , nonlinear system , diffusion , oscillation (cell signaling) , traveling wave , initial value problem , population , mathematics , reaction–diffusion system , statistical physics , mathematical analysis , physics , computer science , chemistry , thermodynamics , biochemistry , demography , quantum mechanics , sociology , operating system
A multiple time scale procedure is developed and used to describe the full transient behavior of solutions to certain classes of nonlinear diffusion initial value problems where the diffusion coefficients are in a certain sense “weak.” Specific examples are presented which demonstrate the explicit manner in which various traveling wave and oscillation patterns develop from arbitrary initial data for certain well‐known model systems in population biology and chemical kinetics.