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

Authors:	Thierry Horsin Molinaro

Institution:	1. Mission fran?aise de coopération, BP 1839, Abidjan 01, (République de C?te d'Ivoire) 2. CMLA ENS Cachan, 61 avenue du président Wilson, 94235, Cachan cedex, (France) 3. Laboratoire d'analyse numérique, Université Paris Sud, 91400, Orsay Cedex, (France)

Abstract:	This paper is concerned with the evolution of harmonic maps from an open set Ω of ℝ^m 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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