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Long-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid

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Abstract

This paper is concerned with the evolution of harmonic maps from an open set Ω of ℝm into an n-dimensionnal ellipsoid\(N = \left\{ {u = (u_I ,u_{II} ) \in \mathbb{R}^n \times \mathbb{R}/u_I^2 + \frac{{u_{II}^2 }}{{a^2 }} = 1} \right\}\) where a ∈ (0, 1]

We prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact subset of the upper hemisphere of an ellispoid.

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Authors and Affiliations

  1. Mission française de coopération, BP 1839, Abidjan 01, (République de Côte d'Ivoire)

    Thierry Horsin Molinaro

  2. CMLA ENS Cachan, 61 avenue du président Wilson, 94235, Cachan cedex, (France)

    Thierry Horsin Molinaro

  3. Laboratoire d'analyse numérique, Université Paris Sud, 91400, Orsay Cedex, (France)

    Thierry Horsin Molinaro

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  1. Thierry Horsin Molinaro
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Horsin Molinaro, T. Long-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid. Manuscripta Math 78, 317–333 (1993). https://doi.org/10.1007/BF02599316

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  • DOI: https://doi.org/10.1007/BF02599316

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