English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We discuss the minimal integrability needed for the initial data, in orderthat the Cauchy problem for a multi-dimensional conservation law admit anentropy solution. In particular we allow unbounded initial data. We investigatealso the decay of the solution as time increases, in relation with thenonlinearity. The main ingredient is our recent theory of divergence-freepositive symmetric tensor. We apply in particular the so-called compensatedintegrability to a tensor which generalizes the one that L. Tartar used in onespace dimension. It allows us to establish a Strichartz-like inequality, in aquasilinear context. This program is carried out in details for amulti-dimensional version of the Burgers equation.

Multi-dimensional scalar conservation laws with unbounded integrable initial data