Complex Ginzburg–Landau Equation with Absorption: Existence, Uniqueness and Localization Properties

Abstract

In this paper we study the time-dependent complex Ginzburg–Landau equation with a nonlinear absorbing term in \({\Omega \times(0,T),\, \Omega }\) open bounded set in \({\mathbb{R}^{n}}\) . We prove global existence and uniqueness of solutions for the initial and boundary-value problem and study the properties of localization and extinction of solutions in some special cases.

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Correspondence to Stanislav Antontsev.

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Dedicated to Professor Hugo Beirão da Veiga on his 70th birthday

This work was completed with the support of our \({{\rm T_{E}X}}\)-pert.

Communicated by G.P.Galdi

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Antontsev, S., Dias, J. & Figueira, M. Complex Ginzburg–Landau Equation with Absorption: Existence, Uniqueness and Localization Properties. J. Math. Fluid Mech. 16, 211–223 (2014). https://doi.org/10.1007/s00021-013-0147-0

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Mathematics Subject Classification (2010)

  • 35 K15
  • 35 B40
  • 35Q35

Keywords

  • Ginzburg–Landau equation
  • absorption
  • localization
  • extinction