On uniform attractors of explicit approximations (Q647687)

The authors prove a theorem on the upper semicontinuous dependence on the parameter of the uniform attractors of a family of semiprocesses not necessarily having a common time semigroup. For a nonautonomous system of ordinary differential equations an explicit finite-difference scheme is suggested showing the existence of its attractor which lies in any neighborhood of the attractor of the original differential equation system for sufficiently small grid increments. Also for the vorticity equation on a rotating sphere with time-dependent bounded right-hand-side a finite-difference scheme is considered for which the existence of a uniform attractor is proved, approximating the true attractor of the original equation when the discretization parameter tends to zero.