The global existence and attractor for p-Laplace equations in unbounded domains

摘要

The asymptotic behavior for a class of parabolic p-Laplace equations in an open bounded or unbounded domain of R-N is investigated. Based on a general condition on the nonlinearity f(x, u) and the invading domain technique, the global well-posedness of the equation is established. By proving the omega-limit compactness of the continuous semigroup, the existence of the global attractor for the equation is obtained. Besides, in case of bounded domains, we also get estimates of the finite fractal dimension of the global attractor based on the classical method of l-trajectories.