Visintin: On a class of doubly nonlinear evolution equations

Abstract. The abstract equation A du dt +Bu 3 f is considered for A and B nonlinear maximal monotone operators in a Hilbert space H, with A bounded, B unbounded and such that its domain D(B) is contained in a Banach space V compactly embedded in H. Existence results are proved for the related initial-value problem, requiring that either A or B be the subdifferential of a convex and lower semicontinuous function, and assuming suitable coerciveness conditions. Arguments are based on monotonicity and compactness techniques. Key words: nonlinear evolution equations, maximal monotone operators, initial-value problems