Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension

Abstract

By extending the concept of the Liapunov functional and an idea due to Dafermos we establish an Invariance Principle for a class of (not necessarily strongly) monotone systems. This principle is then applied to continuous contraction, strongly monotone systems on a Hubert space and to a class of L 1 contraction monotone semigroups generated by degenerate equations in divergence form in one space dimension.