A simple derivation of BV bounds for inhomogeneous relaxation systems

Abstract : We consider relaxation systems of transport equations with heterogeneous source terms and with boundary conditions, which limits are scalar conservation laws. Classical bounds fail in this context and in particular BV estimates. They are the most standard and simplest way to prove compactness and convergence. We provide a novel and simple method to obtain partial BV regularity and strong compactness in this framework. The standard notion of entropy is not convenient either and we also indicate another, but closely related, notion. We give two examples motivated by renal flows which consist of 2 by 2 and 3 by 3 relaxation systems with 2-velocities but the method is more general.
Document type :
Journal articles
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00974269
Contributor : Magali Tournus <>
Submitted on : Sunday, April 6, 2014 - 4:26:11 PM
Last modification on : Friday, January 10, 2020 - 4:28:04 PM
Long-term archiving on: Sunday, July 6, 2014 - 10:37:54 AM

Files

RelaxationPST_Arxiv.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00974269, version 1
  • ARXIV : 1404.1604

Citation

Benoît Perthame, Nicolas Seguin, Magali Tournus. A simple derivation of BV bounds for inhomogeneous relaxation systems. Communications in Mathematical Sciences, International Press, 2014, 13 (2), pp.577-586. ⟨hal-00974269⟩

Share

Metrics

Record views

1039

Files downloads

295