Journal of Dynamics and Differential Equations

, Volume 10, Issue 1, pp 1–35

Existence of Standing Pulse Solutions to an Inhomogeneous Reaction–Diffusion System

  • Christopher K. R. T. Jones
  • Jonathan E. Rubin
Article

DOI: 10.1023/A:1022651311294

Cite this article as:
Jones, C.K.R.T. & Rubin, J.E. Journal of Dynamics and Differential Equations (1998) 10: 1. doi:10.1023/A:1022651311294

Abstract

We prove the existence of locally unique, symmetric standing pulse solutions to homogeneous and inhomogeneous versions of a certain reaction–diffusion system. This system models the evolution of photoexcited carrier density and temperature inside the cavity of a semiconductor Fabry–Pérot interferometer. Such pulses represent the fundamental nontrivial mode of pattern formation in this device. Our results follow from a geometric singular perturbation approach, based largely on Fenichel's theorems and the Exchange Lemma.

Standing wavesinhomogeneous reaction–diffusion systemgeometric singular perturbationsemiconductor Fabry–Pérot interferometer

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Christopher K. R. T. Jones
    • 1
  • Jonathan E. Rubin
    • 2
  1. 1.Division of Applied MathematicsBrown University, ProvidenceRhode Island
  2. 2.Department of MathematicsThe Ohio State UniversityColumbus