  We consider a multi-dimensional scalar wave equation with memory
corresponding to the viscoelastic material described by a generalized Zener
model. We deduce that this relaxation system is an example of a non-strictly
hyperbolic system satisfying Majda's block structure condition. Well-posedness
of the associated Cauchy problem is established by showing that the symbol of
the spatial derivatives is uniformly diagonalizable with real eigenvalues. A
long-time stability result is obtained by plane-wave analysis when the memory
term allows for dissipation of energy.
