Entropy formulation for fractal conservation laws
- First Online:
- Cite this article as:
- Alibaud, N. J. evol. equ. (2007) 7: 145. doi:10.1007/s00028-006-0253-z
- 203 Views
Using an integral formula of Droniou and Imbert (2005) for the fractional Laplacian, we define an entropy formulation for fractal conservation laws with pure fractional diffusion of order λ ∈]0, 1]. This allows to show the existence and the uniqueness of a solution in the L∞ framework. We also establish a result of controled speed of propagation that generalizes the finite propagation speed result of scalar conservation laws. We finally let the non-local term vanish to approximate solutions of scalar conservation laws, with optimal error estimates for BV initial conditions as Kuznecov (1976) for λ = 2 and Droniou (2003) for λ ∈]1, 2].