Archive for Rational Mechanics and Analysis

, Volume 182, Issue 2, pp 181–221

Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling

  • Juan Dávila
  • Manuel del Pino
  • Monica Musso
  • Juncheng Wei
Article

DOI: 10.1007/s00205-006-0421-x

Cite this article as:
Dávila, J., Pino, M., Musso, M. et al. Arch Rational Mech Anal (2006) 182: 181. doi:10.1007/s00205-006-0421-x

Abstract

We consider the boundary value problem

https://static-content.springer.com/image/art%3A10.1007%2Fs00205-006-0421-x/MediaObjects/s00205-006-0421-xflb1.gif

where Ω is a smooth and bounded domain in ℝ2 and λ > 0. We prove that for any integer k ≧ 1 there exist at least two solutions uλ with the property that the boundary flux satisfies up to subsequences λ → 0,

https://static-content.springer.com/image/art%3A10.1007%2Fs00205-006-0421-x/MediaObjects/s00205-006-0421-xflb2.gif

where the ξj are points of ∂Ω ordered clockwise in j.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Juan Dávila
    • 1
  • Manuel del Pino
    • 1
  • Monica Musso
    • 2
    • 3
  • Juncheng Wei
    • 4
  1. 1.Departamento de Ingeniería Matemática and CMMUniversidad de ChileSantiagoChile
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  3. 3.Departamento de MatemáticaPontificia Universidad Catolica de ChileMaculChile
  4. 4.Department of MathematicsThe Chinese University of Hong-KongHong Kong