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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i4.60
pages 481-498

Complexification in Sensitive Singular Perturbations and Their Appproximation

C. A. De Souza
Department of Mechanical Engineering, Federal University of Brasilia, Brasilia, 70910-900, Brazil
Evariste Sanchez-Palencia
Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie 4, place Jussieu, Paris, 75252, France

ABSTRACT

We consider a type of singular perturbation boundary value problem depending on a parameter ε that is classical for ε > 0 but highly ill posed for ε = 0. This kind of problem arises from thin shell theory; but here, we only deal with a model problem allowing a Fourier transform treatment. The asymptotic process exhibits a complexification phenomenon: in some sense, the solution becomes more and more complex as ε decreases. This phenomenon is associated with the emergence of a new characteristic parameter log ε−1. We also give an approximate heuristic method and we verify its reliability.


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