On nonlinear hyperbolic evolution equations with unilateral conditions dependent on time (Q5903143)

The author considers the strong solution of the following nonlinear hyperbolic evolution equation \[ d^ 2u(t)/dt^ 2+A u(t)+\partial I_{K(t)}(du(t)/dt)\ni f(t),\quad 0\leq t\leq T \] in a real Hilbert space H. Here A is a positive self-adjoint operator in H. For each \(t\in [0,t]\), K(t) is a closed convex subset of H and \(\partial I_{K(t)}\) is the subdifferential of \(I_{K(t)}\) which is the indicator function of K(t).