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Abstract: "We study the equations of viscoelasticity in a multidimensional setting for the 'no-traction' boundary data. For the sake of modeling phase transitions we do not assume ellipticity of the stored energy function W. We construct dynamics in W[superscript 1,2]([omega], r[superscript n]) globally in time. Next, we study the question of stability for a class of equilibria. Moreover, we show certain kind of decay in time of solutions for arbitrary initial conditions."