Set-valued pseudomonotone maps and degenerate evolution inclusions

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are (Bu)' + Au 3 f, where B = B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems. We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution. This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.