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Singularly Perturbed Boundary-Value Problems
It is well known that many phenomena in biology, chemistry, engineering, physics canbedescribedbyboundaryvalueproblemsassociatedwithvarioustypes ofp- tial di?erential equations or systems. When we associate a mathematical model with a phenomenon, we generally try to capture what is essential, retain...
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| Auteurs principaux : | , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Singularly Perturbed Boundary-Value Problems / Luminiţa Barbu and Gheorghe Moroşanu. |
| Édition : | 1st ed. 2007. |
| Publié : |
Basel :
Birkhäuser Basel
, [20..] Cham : Springer Nature |
| Collection : | International series of numerical mathematics (Online) ; 156 |
| Accès en ligne : |
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Preliminaries. Regular and Singular Perturbations. Evolution Equations in Hilbert Spaces. Singularly Perturbed Hyperbolic Problems. Presentation of the Problems. Hyperbolic Systems with Algebraic Boundary Conditions. Hyperbolic Systems with Dynamic Boundary Conditions. Singularly Perturbed Coupled Boundary Value Problems. Presentation of the Problems. The Stationary Case. The Evolutionary Case. Elliptic and Hyperbolic Regularizations of Parabolic Problems. Presentation of the Problems. The Linear Case. The Nonlinear Case |
| Sujets : | |
| Documents associés : | Autre format:
Singularly perturbed Boundary-Value problems |
| Résumé : | It is well known that many phenomena in biology, chemistry, engineering, physics canbedescribedbyboundaryvalueproblemsassociatedwithvarioustypes ofp- tial di?erential equations or systems. When we associate a mathematical model with a phenomenon, we generally try to capture what is essential, retaining the important quantities and omitting the negligible ones which involve small par- eters. The model that would be obtained by maintaining the small parameters is called the perturbed model, whereas the simpli?ed model (the one that does not includethesmallparameters)iscalledunperturbed(orreducedmodel). Ofcourse, the unperturbed model is to be preferred, because it is simpler. What matters is that it should describefaithfully enoughthe respectivephenomenon, which means that its solution must be close enough to the solution of the corresponding perturbed model. This fact holds in the case of regular perturbations (which are de?ned later). On the other hand, in the case of singular perturbations, things get morecomplicated. If we refer to aninitial-boundary value problem,the solutionof theunperturbed problemdoes notsatisfy ingeneralallthe originalboundary c- ditions and/or initial conditions (because some of the derivatives may disappear byneglecting the small parameters). Thus, somediscrepancymay appear between the solution of the perturbed model and that of the corresponding reduced model. Therefore, to ?ll in this gap, in the asymptotic expansion of the solution of the perturbed problem with respect to the small parameter (considering, for the sake of simplicity, that we have a single parameter), we must introduce corrections (or boundary layer functions). Morethanhalfacenturyago,A. N |
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| Notes : | L'impression du document génère 237 p. |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-3-7643-8331-2 |
| DOI : | 10.1007/978-3-7643-8331-2 |