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 typewith −∞ < 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) = ϕ(x) decays faster than polinomially on IR + = { x ∈ IR ; x > 0 } and has certain initial Sobolev regularity.