Title: Long-time existence of nonlinear inhomogeneous compressible elastic waves,
Abstract: In this paper, we consider the nonlinear inhomogeneous compressible elastic
waves in three spatial dimensions when the density is a small disturbance
around a constant state. In homogeneous case, the almost global existence was
established by Klainerman-Sideris [1996_CPAM], and global existence was built
by Agemi [2000_Invent. Math.] and Sideris [1996_Invent. Math., 2000_Ann. Math.]
independently. Here we establish the corresponding almost global and global
existence theory in the inhomogeneous case.