**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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