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arXiv: nlin.SI/0304014

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Functional sensitivity of Burgers and related equations to initial conditions

Olivier Vallée 1

(2003-04-09)

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 resultstands in the fact that the most the solution is sensitive to theinitial 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.

1:	Laboratoire d'Analyse Spectroscopique et d'Energétique des Plasmas (LASEP - EA3269)
	Université d'Orléans

Subject

:

Nonlinear Sciences/Exactly Solvable and Integrable Systems

Keyword(s): Burgers equation – KPZ equation – sensitivity to initial conditions – sensitivity analysis – turbulence.

hal-00000296, version 1

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From: Olivier Vallée <>

Submitted on: Wednesday, 9 April 2003 18:26:42

Updated on: Thursday, 10 April 2003 08:30:59