Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (4): 906-944.doi: 10.1016/S0252-9602(15)30028-X

• Articles • Previous Articles     Next Articles

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.

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

CLC Number: 

  • 35L50
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