Jem. Rivera et Lh. Fatori, SMOOTHING EFFECT AND PROPAGATIONS OF SINGULARITIES FOR VISCOELASTIC PLATES, Journal of mathematical analysis and applications, 206(2), 1997, pp. 397-427
We study dissipative models for plates and we show that the solutions
have a smoothing effect on the initial data for viscous plates, while
for materials with memory the solution propagates singularities, that
is, the solution of the plate equation of memory type is as regular as
the initial data. Moreover, we show that when both dissipations are p
resent, the memory type prevails in the sense that the solution propag
ates singularities. Finally, we prove the existence of global solution
s for non-linear dissipative equations, with small data, which decay e
xponentially as time goes to infinity. (C) 1997 Academic Press.