World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
Our website is made possible by displaying certain online content using javascript.
In order to view the full content, please disable your ad blocker or whitelist our website

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

On a quadratic functional for scalar conservation laws

    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.

    AMSC: 35L65