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On the appropriate treatment of singularly perturbed wave equations
Author(s) -
Schagerl M.,
Berger A.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20010811588
Subject(s) - sort , singular perturbation , perturbation (astronomy) , type (biology) , point (geometry) , mathematics , calculus (dental) , mathematical analysis , mathematical economics , physics , geometry , geology , arithmetic , medicine , dentistry , quantum mechanics , paleontology
Engineers frequently find themselves concerned with the following situation: One is not interested in certain effects of a model, expecting them to have no significant influence, and one therefore simply neglects them‐even if the type of the governing equations is changed. Having obtained a sound knowledge about the thus simplified problem one would nevertheless like to take into account the effects neglected at first, preferably as some sort of small perturbation. By means of an example from dynamics we point out that such an approach may necessitate some careful analysis: More often than not the perturbations turn out to be of rather singular type.