Large-time behaviour of solutions of the inviscid non-planar Burgers equation

摘要

Large-time behaviour of the entropy solution of an initial-value problem (IVP) for the inviscid non-planar Burgers equation is studied. The initial profile is assumed to be non-negative, bounded and compactly supported. The large-time behaviour of the support function of this entropy solution is also presented. This is achieved via the construction of the entropy solution of the IVP for the inviscid non-planar Burgers equation subject to the top-hat initial condition using the method of characteristics, Rankine-Hugoniot jump condition, and a similarity solution.