Solvability and long time behavior of nonlinear reaction–diffusion equations with Robin boundary condition

In this paper, we investigate the long-time behavior and solvability of the reaction–diffusion equation, which has a polynomial growth nonlinearity of arbitrary order, with Robin boundary condition. We begin this paper with the existence and uniqueness of the solution to the problem. For the long-time behavior, we firstly prove the existence of an absorbing set in two different spaces. Secondly, for the autonomous case, the existence of a global attractor is obtained in W21(Ω)∩Lρ+2(Ω).