Rodríguez Bernal, AníbalWillie, Robert2023-06-202023-06-202007-07-010362-546X10.1016/j.na.2006.05.017https://hdl.handle.net/20.500.14352/50283We study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations. A priori, we review both local and global dynamics of the system in scales of Banach spaces of Hilbert type and we prove the existence of a universal compact attractor for the equations. Extensions yield the existence of a family of nesting inertial manifolds dependent on the diffusion of the system of equations. It is introduced an upper semicontinuity notion in large diffusivity for inertial manifolds. The limit inertial manifold whose dimension is strictly less than those of the infinite dimensional system of semilinear evolution equations is obtained.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0362546X06003233http://www.sciencedirect.com/restricted access517.986Semilinear system of reaction-diffusion equationsWell posednessUniversal compact attractorInertial manifoldsLimit inertial manifoldLarge diffusivityFunciones (Matemáticas)1202 Análisis y Análisis Funcional