Some remarks concerning the one-dimensional Burgers equation

Abstract

The behaviour of solutions of the Burgers system (1)—(3) is studied. In earlier papers [4], [5] the problem of the global stability of the constant solution (17, v) = ^ v “ , oj when < v was solved. The behaviour of those solutions (17,v) which do not converge to the constant solution when t tends to infinity is studied here. In part 3 some of its properties are studied, while in parts 2 and 4 several a priori estimates needed in the proof of existence of solutions are presented.