Finite-dimensional attractor for the laser equations

Peter Constantin, C. Foias, J. D. Gibbon

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The laser equations of Risken and Nummedal (1968) govern the dynamics of a ring laser cavity. They form a system of hyperbolic, semilinear, damped and driven partial differential equations with periodic boundary conditions. The Lorenz system of ordinary differential equations is an invariant subsystem of the laser equations corresponding to solutions without spatial dependence. The authors prove that the laser system admits global weak solutions for arbitrary L2 initial data. Despite the absence of parabolic diffusion they prove that the laser system enjoys a remarkable property of hyperbolic smoothing for t to infinity : the universal attractor for the L2 evolution consists of Cinfinity functions. They show, moreover, that the universal attractor is finite dimensional and estimate its dimension.

Original languageEnglish (US)
Pages (from-to)241-269
Number of pages29
JournalNonlinearity
Volume2
Issue number2
DOIs
StatePublished - May 1989

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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