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We prove the well-posedness and decay of Besicovitch almost periodic solutions for nonlinear degenerate anisotropic hyperbolic-parabolic equations. We also investigate the case where the diffusion term is given by a non-degenerate nonlinear $d"\X d"$ diffusion matrix and the complementary $d'$ components of flux-function form a non-degenerate flux in $\R^{d'}$, with $d'+d"=d$. For this special case we prove that the strong trace property at the initial time holds, which allows to require the assumption of the initial data only in a weak sense, as well as the continuity in time of the solution with values in $L_\loc^1(\R^d)$.

On the decay of almost periodic solutions of anisotropic degenerate parabolic-hyperbolic equations