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Preprint 2013-011

On a quadratic functional for scalar conservation laws

Stefano Bianchini and Stefano Modena

Abstract: We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

The proof is based on the introduction of a quadratic functional Q(t), decreasing at every interaction, and such that its total variation in time is bounded.

Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case.

Paper:
Available as PDF (668 Kbytes).
Author(s):
Stefano Bianchini
Stefano Modena
Submitted by:
; 2013-11-12.