Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity

We consider the problem of uniform long-time behavior of all globally defined weak solutions of a non-autonomous reaction–diffusion system with Carathéodory’s nonlinearity satisfying standard sign and polynomial growth assumptions. The main contributions of this paper are: (i) the existence of a uniform trajectory attractor for all globally defined weak solutions of non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity, (ii) sufficient conditions for the existence of a uniform trajectory attractor in strongest topologies, and (iii) new topological properties of weak solutions.