Ricerc@Sapienza

Given A, Bin R^n imes n, we consider the Cauchy problem for partially dissipative hyperbolic systems having the form partiatl_t u+Apartial_x u+Bu = 0, with the aim of providing a detailed description of the large-time behavior. Sharp Lp-Lq estimates are established for the distance between the solution to the system and a time-asymptotic profile, where the profile includes a solution to a parabolic system and a solution of a hyperbolic system. The key tools for the proof are the Fourier transform together with the Young inequality and the interpolation inequality.