Relaxation approximation of Friedrichs' systems under convex constraints

Jean-François  Babadjian; Clément  Mifsud; Nicolas Seguin; Jean-François  Babadjian; Clément  Mifsud; Nicolas Seguin

doi:10.3934/nhm.2016.11.223

Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 223-237. doi: 10.3934/nhm.2016.11.223

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Relaxation approximation of Friedrichs' systems under convex constraints

1.
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris
2.
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris

Received: 01 April 2015 Revised: 01 September 2015
Primary: 35L45, 35L60; Secondary: 35A35.

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in $L^2_{\text{loc}}$ of a parabolic-relaxed approximation towards the unique constrained solution.
- Friedrichs' systems,
- convex constraints
Citation: Jean-François Babadjian, Clément Mifsud, Nicolas Seguin. Relaxation approximation of Friedrichs' systems under convex constraints[J]. Networks and Heterogeneous Media, 2016, 11(2): 223-237. doi: 10.3934/nhm.2016.11.223

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Abstract

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in $L^2_{\text{loc}}$ of a parabolic-relaxed approximation towards the unique constrained solution.

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