The authors investigate the existence of a global attractor for the reaction diffusion problem
where , , is a smooth bounded domain, and is a function of class satisfying the following conditions: There exist and positive constants , and such that for all , , and .
It is shown that the semigroup generated by this problem possesses a global attractor in which is invariant, compact in with
and attracting every bounded subset of in the norm of with . The proof is done by a decomposition technique combined with a bootstrap argument to establish some regularity results on the solutions.
The decomposition scheme involves the existence and uniqueness of solutions for the original problem (RD) to obtain regularity results for which satisfies
where satisfies the elliptic equation with homogeneous Dirichlet boundary condition and for .