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Long time behavior of a third order (in time) nonlinear PDE equation is considered. This type of equations arises in the context of nonlinear acoustics [12, 21, 24] where modeling accounts for a finite speed of propagation paradox, the latter results in hyperbolic nature of the dynamics. It will be proved that the underlying PDE generates a wellposed dynamical system which admits a global and finite dimensional attractor. The main difficulty associated with the problem studied is the lack of Lyapunov function along with the lack of compactness of trajectories, which fact prevents applicability of standard tools in the area of dynamical systems.

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