Kernel sections and uniform attractors of multi-valued semiprocesses

We present the existence of kernel sections (which are all compact, invariant and pullback attracting) of an infinite-dimensional general multi-valued process constructed by the set-valued backward extension of multi-valued semiprocesses. Moreover, the structure of the uniform attractors of a family of multi-valued semiprocesses and the uniform forward attraction of kernel sections of a family of general multi-valued processes are investigated. Finally, we explain our abstract results by considering the mixed wave systems with supercritical exponent and ordinary differential equations.