We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinity. Our results improve the earlier ones since we only require the flux to be nonlinear at the mean value of the initial data.
Travelling waves of Burgers Fisher equation are shown to be stable in exponentially weighted L ∞ spaces, here we only consider the monotone travelling wave. The method uses the spectral analysis of the linearized equation.
