A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem

摘要: We study a semilinear hyperbolic problem, written as second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly terms data. Despite elementary character, our technique gives reasonable results. Notably, require no additional regularity, although nonlinear damping is allowed.