Some Properties Of The Solutions To A Class Of Shallow Water Equations

In this paper, we study some properties of solutions to the Cauchy problem of aclass of shallow water wave equations arising from modern mechanics and physics. Inthe first place, we give a brief introduction about the background of shallow water waveequations, which includes some results obtained by other authors in this field.Subsequently, we introduce the basic concepts of problems discussed in this thesis andresearch methods we used later. In Chapter3, we focus on the existence and uniquenessof local solutions to a class of shallow water wave equations and blow-up phenomena.In Chapter4, we use the energy method and differential inequalities to deal with theNovikov equation with strong dissipative term; the local well-posedness of the solutionis established.