Optimal decay rates for the system of elastic waves in R~n with structural damping

摘要

We consider the Cauchy problem in R~n for the system of elastic waves with structural damping. We derive (almost) optimal decay rates in time for the L~2-norm and the total energy which improves previous results for this system. To derive the estimates for elastic waves, we employ an improvement in a method in the Fourier space, which was developed in our previous works. Our estimates came from those for a generalized energy of α-order in the Fourier space.