Lagrangian for the convection-diffusion equation

Jacky Cresson (1) , Isabelle Greff (1) , Pierre Inizan (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

Using the asymmetric fractional calculus of variations, we derive a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.

Keywords: Lagrangian structure; Fractional derivatives; Convection-diffusion equation

Domains: Analysis of PDEs [math.AP]; Dynamical Systems [math.DS]

Jacky Cresson, Isabelle Greff, Pierre Inizan. Lagrangian for the convection-diffusion equation. Mathematical Methods in the Applied Sciences, 2012, 35 (15), pp.1885--1895. ⟨10.1002/mma.2651⟩. ⟨hal-00651826⟩