On the Cauchy problem for scalar conservation laws on the Bohr compactification of \Rⁿ

2014/08/04 by Evgeny Yu. Panov, Panov, Evgeny Yu.
Mathematics · Physics and Astronomy · #35L65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:35L65

paper · pdf · doi:10.48550/arxiv.1408.0658

arxiv created 2014/08/04 · openalex publication_date 2014/08/04 · arxiv updated 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Cauchy problem for a multidimensional scalar conservation law on the Bohr compactification of \Rⁿ. The existence and uniqueness of entropy solutions are established in the general case of merely continuous flux vector. We propose also the necessary and sufficient condition for the decay of entropy solutions as time t→+∞.

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