Uniform attractors of dynamical processes and non-autonomous equations of mathematical physics

Abstract

Uniform attractors are investigated for dynamical systems corresponding to non-autonomous partial differential equations. The problem reduces to an analysis of families of dynamical processes (when the original equation is defined on the whole time axis) or dynamical semiprocesses (when it is defined on a half-axis). Results are established on the existence of uniform global attractors for families of processes and semiprocesses. The structure of attractors for non-autonomous equations with translation-compact symbols is investigated. Conditions are found under which attractors of semiprocesses reduce to attractors of corresponding processes. An important special case of equations with asymptotically almost periodic terms is examined. Several examples of non-autonomous equations of mathematical physics are considered, uniform global attractors are constructed in these examples, and their structure is studied.Bibliography: 28 titles.