Functional sensitivity of Burgers and related equations to initial conditions

Abstract

In this paper, we apply sensitivity methods to nonlinear PDEs like Burgers and KPZ equations. These equations are known to have analytical solutions which make easier the analysis of the sensitivity of their solutions to initial conditions. The main result stands in the fact that the most the solution is sensitive to the initial condition, the most it is decorrelated in space, i.e. the values of the initial condition participate to the solution at all distances of the wave front. This finally reveals a particular aspect of the Burgers turbulence.