Gain of regularity for an nonlinear dispersive equation korteweg - de vries-burgers type

Abstract

In this papers we study smoothness properties of solutions. We consider the equation of Korteweg - de Vries - Burgers type:(1)öut+@xf(u)=è @2xuÄé @3xu(x;0) ='(x) with Ä1< x <+1andt >0: The flux f=f(u)is a given smooth function satisfying certain assumptions to be listed shortly. It is shown under certain additional conditions on f that C1- solutions u(x; t) are obtained for all t >0 if the initial data u(x;0) ='(x) decays faster than polinomially on IR +=fx2IR;x 0 and has certain initial Sobolev regularity.