A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain

Tools

Kellogg, R. Bruce and Kopteva, Natalia (2010) A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain. Journal of Differential Equations, 248 (1). pp. 184-208. ISSN 0022-0396 (https://doi.org/10.1016/j.jde.2009.08.020)

[thumbnail of kellogg_kopt_poly.pdf]
Preview
 PDF. Filename: kellogg_kopt_poly.pdf
Preprint
Download (295kB)| Preview

Abstract

The semilinear reaction-di®usion equation ¡"24u+b(x; u) = 0 with Dirichlet bound-ary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation” b(x, u0 (x)) = 0 may have multiple solutions. An asymptotic expansion for u is constructed that involves boundary and corner layer functions. By perturbing this asymptotic expansion, we obtain certain sub- and super-solutions and thus show the existence of a solution u that is close to the constructed asymptotic expansion. The polygonal boundary forces the study of the nonlinear autonomous elliptic equation −Dz + f (z) = 0 posed in an infinite sector, and then well-posedness of the corresponding linearized problem.

  • Item type:Article
    ID code:44818
    Dates:
    Date
    Event
    1 January 2010
    Published
    11 September 2009
    Published Online
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:12 Sep 2013 14:47
    Last modified:12 Dec 2024 02:50
    URI:https://strathprints.strath.ac.uk/id/eprint/44818
CORE (COnnecting REpositories)