Homographic approximation for some nonlinear parabolic unilateral problems (Q2718675)

This paper deals with nonlinear parabolic unilateral problems by means of the homographic approximation introduced by C. M. Brauner and B. Nicolaenko in the linear elliptic case. The nonlinear operator is a coercive, continuous, and pseudomonotone operator of Leray-Lions type, acting from \(L^p(0,T; W^{1,p}_0(\Omega))\) into its dual, \(\Omega\) is an open bounded set of \(\mathbb{R}^N\), \(N\geq 2\). The existence and the uniqueness of the strong solution of a variational inequality with obstacle admitting ``downward jumps'' is proved and a dual esimate of Lewy-Stampacchia type is established. The obstacle problems with \(L^1\) data are also considered, existence and uniqueness results of the ``entropy'' solution as well as Lewy-Stampacchia type inequality are established.