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