On the uniformly continuity of the solution map for two dimensional wave maps

S. Georgiev, University of Sofia, Sofia, Bulgaria
P. Georgieva, University of Sofia, Sofia, Bulgaria

E. J. Qualitative Theory of Diff. Equ., No. 18. (2003), pp. 1-7.

Communicated by V. Lakshmikantham. Appeared on 2003-10-10

Abstract: The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map is not uniformly continuous.

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