The stability of the shock profiles of the Burgers' equation

AbstractIn this paper, we study the existence and stability of the shock profiles of the Burgers' equation, ut + uux = uxx. We make use of Hopf-Cole transformations to show when such profiles exist, to prove that perturbations of the profiles decay exponentially quickly in an exponentially weighted norm, and to demonstrate that making the weight too large does not generally increase the rate of decay of the perturbation