Abstract
In the paper long-time behavior of solutions derived from the dissipative MKdV equation in the unbounded domain is studied. The Sobolev interpolation inequality and prior estimate on time t are applied to show the existence of solution in unbounded domain. Moreover, operator decomposition techniques and Kuratowskii α -noncompacted measures are applied to study the smooth property of the solution. Existence of global attractor for dissipative MKdV equation in H 2 ( R 1 ) is proved. Then, the computational stability of universal double-time differential format is proved by using nature analysis approach and dissipative conservative scheme theory. Finally, accordant conclusion with theoretical proof is drawn by numerical simulation.
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