Periodic and almost periodic solutions of conservation laws: Global existence and decay

  • Hermano Frid

Abstract

In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBVloc and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9].

Key words

conservation laws parabolic equations almost periodic functions 

Mathematical subject classification

Primary 35L65 Secondary 35B35 35B40 

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Copyright information

© Sociedade Brasileira de Matemática 2001

Authors and Affiliations

  • Hermano Frid
    • 1
  1. 1.Instituto de Matemática Pura e Aplicada-IMPARio de JaneiroBrasil

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