Asymptotic Compactness Control for a Class of Nonhomemade Systems with Supercritical Conditions

By means of operator decomposition, the solution operator is decomposed into compact and asymptotically small parts, and truncation function or weighting function is used to prove that the solution is uniformly small for large space and time variables. The asymptotic compactness is proved by means of energy perturbation and the solution operator is decomposed into compact and asymptotically small parts by means of operator decomposition.