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

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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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Authors and Affiliations

  1. CMAF/UL, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    Stanislav Antontsev, João-Paulo Dias & Mário Figueira

Authors
  1. Stanislav Antontsev
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  2. João-Paulo Dias
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  3. Mário Figueira
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Corresponding author

Correspondence to Stanislav Antontsev.

Additional information

Communicated by G.P.Galdi

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.

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Antontsev, S., Dias, JP. & 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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  • DOI: https://doi.org/10.1007/s00021-013-0147-0

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