Inertial Manifolds for Weakly and Strongly Dissipative Hyperbolic Equations

One considers mixed boundary value problems for a quasilinear hyperbolic equation with a weak, as well as strong, dissipation. The nonlinear function in the equation is assumed Lipschitz continuous. For each of these problems one obtains the conditions on the Lipschitz constant that ensure the existence of inertial manifolds.