On the Limit Behavior of the Trajectory Attractor of a Nonlinear Hyperbolic Equation Containing a Small Parameter at the Highest Derivative

We study the trajectory attractor of a nonlinear nonautonomous hyperbolic equation with dissipation depending on a small parameter. The nonlinear function appearing in this equation does not satisfy the Lipschitz condition. It is shown that, as the small parameter tends to zero, the trajectory attractor of the hyperbolic equation converges to the trajectory attractor of the limit parabolic equation in the corresponding topology.