Asymptotics for singular limits via phase functions

Samuel Nordmann, Steve Schochet*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The asymptotic behavior of solutions as a small parameter tends to zero is determined for a variety of singular-limit PDEs. In some cases even existence for a time independent of the small parameter was not known previously. New examples for which uniform existence does not hold are also presented. Our methods include both an adaptation of geometric optics phase analysis to singular limits and an extension of that analysis in which the characteristic variety determinant condition is supplemented with a periodicity condition.

Original languageEnglish
Article number26
JournalNonlinear Differential Equations and Applications
Volume31
Issue number2
DOIs
StatePublished - Mar 2024

Keywords

  • 35B25
  • 35B40
  • Asymptotic behavior
  • Phase function
  • Singular limit

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