Abstract

In this papers we study smoothness properties of solutions. We consider the equation of Korteweg - de Vries - Burgers type (1) {ut + ?xf(u) = ? ?x2 - ? ?x3 u(x, 0) = ?(x) with -? < x < +? and t > 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 C? - solutions u(x, t) are obtained for all t > 0 if the initial data u(x, 0) = ?(x) decays faster than polinomially on IR+ = {x ? IR; x > 0} and has certain initial Sobolev regularity.