Decay Of Solutions Of A Class Of Nonlinear Evolution Equations Initial Estimates

In the past few decades, many people are interested in nonlinear evolution equations, because they were used in physics. Especially, Kortewey de Vries equationand Benjamin-Ono equationThere are lots of literatures about decay estimates of solutions to these equations.The study of this paper originated from Benjamin-Ono Kortewey de Vries equationwhich described Squall line in the atmosphere and whose research background will be addressed in Chapter 1. The standard method-Fourier Splitting will be introduced in detail in Chapter 2. By using developed Fourier Splitting method, it will be proved in the Chapter 3 that L~2 and L~∞norms of the solution to Benjamin-Ono Kortewey de Vries equation with a dissipative termαuxx, tend to zero at certain decay rates as tâ†'∞. The last chapter concludes and outlines for further research.