Existence results for a class of pseudomonotone elliptic-parabolic inclusions

This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB(u)/dt + A(u) f, v0 ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.