Colli, Pierluigi; Savaré, Giuseppe On a class of implicit evolution variational inequalities. (English) Zbl 0844.35058 Differ. Integral Equ. 8, No. 8, 2097-2124 (1995). Let \(V\subset H\subset V'\) be an evolution triple, where \(V\) and \(H\) are Hilbert spaces. The Cauchy problem for the following nonlinear evolution equation \[ (I+ \partial\phi)(u'(t))+ Lu(t) \ni F(t, u(t)),\quad 0<t< T \] is studied. Here \(\partial\phi\) denotes the subdifferential of a proper, convex, and lower-semicontinuous function \(\phi: V\to (- \infty, +\infty]\), \(L: V\to V'\) is a linear, bounded, and selfadjoint operator, and \(F: (0, T)\times V\to V'\) is a nonlinear function. Qualitative results (via finite differences in time) and applications to PDEs are discussed. Reviewer: Gheorghe Moroşanu (Iaşi) MSC: 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 34G20 Nonlinear differential equations in abstract spaces 35K55 Nonlinear parabolic equations Keywords:nonlinear evolution equation; finite differences in time PDFBibTeX XMLCite \textit{P. Colli} and \textit{G. Savaré}, Differ. Integral Equ. 8, No. 8, 2097--2124 (1995; Zbl 0844.35058)