On Regular and Singular Perturbations of the Eigenelements of the Laplacian

R. R. Gadyl’shin ()
Additional contact information
R. R. Gadyl’shin: Bashkir State Pedagogical University

Chapter 14 in Integral Methods in Science and Engineering, Volume 1, 2010, pp 135-148 from Springer

Abstract: Abstract We discuss the concept of singularly perturbed eigenvalue problems for the Laplace operator. Typical problems are the boundary value problems for the eigenvalue equations in bounded domains and the possible perturbations are a small parameter at higher derivatives, small holes, thin slits, thin appendices, frequent alternation of boundary conditions, etc. The main feature of these problems is that there exists no change of variables reducing them to problems in a fixed domain with a regularly perturbed operator. At the same time, the eigenvalues of such singularly perturbed boundary value problems converge to those of certain limiting problems. This is why, in the sense of convergence, the eigenvalues behave in the regular way.

Keywords: Asymptotic Expansion; Bounded Domain; Singular Perturbation; Helmholtz Resonator; Regular Perturbation (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4899-2_14

Ordering information: This item can be ordered from
http://www.springer.com/9780817648992

DOI: 10.1007/978-0-8176-4899-2_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().