Enlarged Numerical Attractors for Lattice Systems with Porous Media Degeneracies

.A positively invariant ball and a global attractor for the porous media lattice system are obtained. By the implicit Euler scheme, the continuous-time model is discretized as a discrete-time porous media lattice system, which generates a discrete semigroup on the positively invariant ball for sufficiently small step sizes. It is shown that the discrete semigroup has a numerical attractor, which converges upper semicontinuously to the global attractor as the step size tends to zero. A new subject on enlarged attractors for lattice systems is investigated, which includes unique existence and convergence of attractors as well as solutions on the larger initial space. The second-order Taylor expansion and discretization error on the enlarged regular space are established to prove the upper semicontinuity of the enlarged numerical attractors with respect to the step size, while an upper bound of the enlarged attractors is provided to establish the lower semicontinuity in special cases.Keywordsporous media degeneracieslattice dynamical systems systemnumerical attractorsenlarged regularityMSC codes35B4037L6065L20