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

Abstract

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.