Skip to main content
padlock icon - secure page this page is secure

Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems

Buy Article:

$59.00 + tax (Refund Policy)

In an arbitrary bounded 2-D domain, a singular perturbation approach is developed to analyze the asymptotic behavior of several biharmonic linear and nonlinear eigenvalue problems for which the solution exhibits a concentration behavior either due to a hole in the domain, or as a result of a nonlinearity that is nonnegligible only in some localized region in the domain. The specific form for the biharmonic nonlinear eigenvalue problem is motivated by the study of the steady-state deflection of one of the two surfaces in a Micro-Electro-Mechanical System capacitor. The linear eigenvalue problem that is considered is to calculate the spectrum of the biharmonic operator in a domain with an interior hole of asymptotically small radius. One key novel feature in the analysis of our singularly perturbed biharmonic problems, which is absent in related second-order elliptic problems, is that a point constraint must be imposed on the leading order outer solution to asymptotically match inner and outer representations of the solution. Our asymptotic analysis also relies heavily on the use of logarithmic switchback terms, notorious in the study of Low Reynolds number fluid flow, and on detailed properties of the biharmonic Green’s function and its associated regular part near the singularity. For a few simple domains, full numerical solutions to the biharmonic problems are computed to verify the asymptotic results obtained from the analysis.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Affiliations: 1: University of Arizona 2: University of British Columbia 3: Simon Fraser University

Publication date: May 1, 2011

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more