  The abstract elliptic and parabolic equations on exterior domain are
considered. The equations have top-order variable coefficients. The
separability properties of boundary value problems for elliptic equation and
well-posedness of the Cauchy problem for parabolic equations are established.
In application, the well-posedness of Wentzell-Robin type mixed probem for
parabolic equation, Cauchy problem for anisotropic parabolic equations and
system of parabolic equations are derived
