**Bárta, Tomáš ^{[1]}**

[1] : Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Prague, Sokolovska 83, 180 00 Prague 8, Czech Republic

**Abstract:**
In this paper we show existence of a global classical solution to a quasilinear
hyperbolic integrodifferential equation of non-convolutionary type for small data. We
apply the result to show global existence for a one-dimensional model of a chemically
reacting viscoelastic body.

This work is supported by GACR 201/09/0917. Author is a researcher in the University Centre for Mathematical Modeling, Applied Analysis and Computational Mathematics (Math MAC) and a member of the Necas Center for Mathematical Modeling.

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