  This paper is concerned with existence and uniqueness of solutions to two
kinds of quasilinear parabolic equations. One is described as the form which
includes the porous media and fast diffusion type equations. The other is the
Cahn--Hilliard type system. The present paper applies Br\'ezis theory directly
to both equations and gives existence results for these two equations even if
the domain is unbounded. Moreover, an error estimate is also proved via apriori
estimates obtained directly.
