On The Large Time Behavior Of Global Weak Solutions To The Degasperis-procesi Equation

For the Cauchy problem of one-dimensional Degasperis-Procesi equation, when theinitial condition u0 belongs to H¹(R) \ L³(R) and (u₀ - u_0,xx) belongs to M⁺(R), itsw^1,∞(R⁺XR)(?)L_loc^∞(R⁺;H¹(R)) global weak solution exists. In this paper, we study thelarge time behavior of such global weak solution.This paper is divided into four parts. In the first part, we give an introduction to theproblem and the state theorem. In the second chapter, we introduce some results whichwe'll use later. In the third chapter, we analyze the large time behavior of the global weaksolution to the Degasperis-Procesi equation. Finally, we conclude with a few questionsfor further investigations.