数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (4): 906-944.doi: 10.1016/S0252-9602(15)30028-X

• 论文 • 上一篇    下一篇

RIGOROUS ESTIMATES ON BALANCE LAWS IN BOUNDED DOMAINS

Rinaldo M. COLOMBO, Elena ROSSI   

  • 收稿日期:2015-03-23 出版日期:2015-07-01 发布日期:2015-07-01
  • 基金资助:

    The present work was supported by the PRIN 2012 project Nonlinear Hyperbolic Partial Differential Equations, Dispersive and Transport Equations: Theoretical and Applicative Aspects and by the INDAM-GNAMPA 2014 project Conservation Laws in the Modeling of Collective Phenomena.

RIGOROUS ESTIMATES ON BALANCE LAWS IN BOUNDED DOMAINS

Rinaldo M. COLOMBO, Elena ROSSI   

  1. 1. Unità INdAM, Università di Brescia, Via Branze 38, 25123 Brescia, Italy;
    2. Dipartimento di Matematica ed Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy
  • Received:2015-03-23 Online:2015-07-01 Published:2015-07-01
  • Supported by:

    The present work was supported by the PRIN 2012 project Nonlinear Hyperbolic Partial Differential Equations, Dispersive and Transport Equations: Theoretical and Applicative Aspects and by the INDAM-GNAMPA 2014 project Conservation Laws in the Modeling of Collective Phenomena.

摘要:

The initial--boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.

关键词: balance laws, initial--boundary value problem for balance laws

Abstract:

The initial--boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.

Key words: balance laws, initial--boundary value problem for balance laws

中图分类号: 

  • 35L50