Oscillations in a dynamical model of phase transitions

The creation and propagation of oscillations in a model for the dynamics of fine structure under viscoelastic damping u(tt) = (u(x)(3) - u(x))(x) + betau(xxt) - alphau, alpha greater than or eq ual to 0, beta > 0 is studied. It is shown that oscillations in the velocity u(t) are lost imm ediately as time evolves, while oscillations in the initial strain u(x) can not be created, and they persist for all time if initially present. Uniquen ess of generalized solutions (Young measures) is obtained, and a characteri zation of these Young measures is provided in the case of periodic modulate d initial data.