Existence Of Rarefaction Wave Solutions Of The Degasperis-Procesi Equation

We consider the global existence of rarefaction wave solutions of the Degasperis-Procesi equation. By rarefaction wave solutions, we mean solutions with given end states, with the left end state less than the right state. We prove the global ex-istence of this kind of solutions to the initial value problem of Degasperis-Procesi equation.This work provides the basis for the study of the nonlinear stability of rar-efaction waves. It reduces the problem to the study of the asymptotic behavior of the weaks solution of a perturbed Degasperis-Procesi equation.This article is divided into 4 chapters. Chapter 1 is introduction. Prelimi-naries needed in the proofs of the conclusions are given in Chapter 2. In Chapter 3, we prove the existence of the global rarefaction wave solutions. Finally, we conclude in Chapter 4 and give some comments on possible future work.