Global Solution and Its Long Time Behavior for the Generalized Long-short Wave Equations (Journal of Partial Differential Equations, 2005)
The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.
Keywords: The generalized long-short wave equations; a uniform priori estimate; global attractor; Hausdorff dimension; fractal dimension