Exponential attractors for reaction–diffusion equations with arbitrary polynomial growth

In this paper, we study exponential attractors for an equation with arbitrary polynomial growth nonlinearity ff and inhomogeneous term gg. First, we prove by the ℓℓ-trajectory method that the exponential attractor in L2(Ω)L2(Ω) with g∈H−1(Ω)g∈H−1(Ω). Second, by proving the semigroup satisfying discrete squeezing property, we obtain the exponential attractor in H01(Ω) with g∈L2(Ω)g∈L2(Ω). Because the solutions without higher regularity than L2p−2(Ω)L2p−2(Ω) for gg belong only to L2(Ω)L2(Ω) in the equation, the general method by proving the Lipschitz continuity between L2p−2(Ω)L2p−2(Ω) and L2(Ω)L2(Ω) does not work in our case. Therefore, we give a new method (presented in a theorem) to obtain an exponential attractor in a stronger topology space i.e., L2p−2(Ω)L2p−2(Ω) with g∈Gg∈G (stated in a definition) when it is out of reach for the other known techniques.