Existence of inertial manifolds for partly dissipative reaction diffusion systems in higher space dimensions

In this paper, we prove the existence of inertial manifolds for a partly dissipative reaction diffusion system of the form u(t) - d Delta u + f(x,u) + g(x,v) = 0, x epsilon Omega v(t) + sigma(x)v + h(x,u) = 0, where Omega is a rectangular domain in R-2 or a cubic domain in R-3. The proof is based on an Abstract Invariant Manifold Theorem for semiflows in a Hilbert space, which is proved by using the graph transform method. The Principle of Spatial Averaging also plays an important role in the proof (C) 1998 Academic Press.