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

A direct approach to quasilinear parabolic equations on unbounded domains by Br\'ezis's theory for subdifferential operators