Long time behaviour for a nonlinear first-order equation Original Research Article

In this paper we study the asymptotic behaviour of solutions to the Cauchy problem for the nonlinear balance law ut+(um)x+um=0ut+(um)x+um=0 with m>1m>1 and bounded, nonnegative, compactly supported initial data. We prove the convergence with a precise rate to a fundamental solution. We also obtain a precise description of the interface.