ASYMPTOTIC INERTIAL MANIFOLD OF SINE-GORDON EQUATION

The numerical results on Sine-Gordon equation show that the dynamical behaviour of this equation is determin.ed by reduced dimensionality. Some theoretic analysis is made on the basis of the fact of dynamics being determined by reduced dimensionality, but this fact has not been proved in mathematics. Ref. [2] has proved that there is a compact attractor with finite Hausdorff dimensions and Fractal dimensions in Sine-Gordon equation. The existenee of inertial manifold of this equation is not yet proved. Ref. [3] gives the proof of nonexistence of inertial manifold in Sine-Gordon equation with weak damp. In this letter, we consider the system