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A small elliptic perturbation of a backward-forward parabolic problem with applications to stochastic models

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
17
Issue
5
Identifiers
DOI: 10.1016/s0893-9659(04)90122-x
Keywords
  • Singular Perturbations
  • Asymptotics
  • Elliptic Pdes
  • Backward-Forward Parabolic Pdes
Disciplines
  • Mathematics

Abstract

Abstract We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markov-modulated queues. We employ singular perturbation methods to study the problem for small values of the parameter.

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