Stability Of Rarefaction Wave For The Scalar Conservation Law With Degenerate Viscosity Under Periodic Perturbation

In this thesis,we mainly consider the large time behavior of the solutions to a scalar conservation law with degenerate viscosity.It is shown that the solution time-asymptotically tends to the rarefaction wave if the initial perturbations are periodic.This thesis has the following three chapters.The first chapter mainly introduces the physical background of the degenerate viscosity studied in this thesis (?)(which can be called Ostwaldde Waele type viscosity)and the research history and current status of related conservation law equations and gives the main conclusions drawn in this thesis as well as the basic concepts and symbols used in this thesis.The second chapter mainly introduces the prerequisite knowledge of this thesis,including several lemmas and some commonly used identities and inequalities.The third chapter is the proof of the main theorem of this thesis.First,the ansatz is constructed.Then the prior estimation is proved by using energy method.Finally,the conclusion is reached.