Asymptotic behaviour of nonlinear parabolic equations with monotone principal part. (Q1873661)

The authors consider abstract evolution problems of the form \(u_t+Au=Bu, \quad u(0)=u_0\), where \(A\) is a maximal monotone operator and \(B\) is a non-monotone (not necessarily Lipschitz) operator defined in a dense subset of a Hilbert space which contains the domain of \(A\). They establish the existence of a global attractor. The main technical point is that the authors have to deal with possible nonuniqueness of solutions. As an application, an equation with \(p\)-Laplacian as the subdifferential operator is examined.