  The well known heat equation with finite speed of propagation proposed by
Cattaneo is obtained by a more general fourth order PDE when a certain (small)
parameters is put equal to zero. It seems that this fourth order equation has
been essentially overlooked in the literature, in particular when it is subject
to non homogeneous boundary conditions. In this paper we examine its well
posedness and the asymptotic behavior when certain coefficients tend to
singular values.
