The paper “Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations” co-authored by  Vladimir Chepyzhov (Russian Academy of Sciences, Moscow), Anna Kostianko, and Sergey Zelik, has been published in the AIMS journal Discrete and Continuous Dynamical Systems B. The paper gives a comprehensive study of inertial manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space.  A link to the published version is here.  A link to the arXiv version is here.  The figure below shows the main theorem of the paper.