# Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients

Bruno Fornet^{[1]}

- [1] LATP, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France LMRS, Université de Rouen, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray, France

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

- Volume: 18, Issue: 2, page 397-443
- ISSN: 0240-2963

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topFornet, Bruno. "Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients." Annales de la faculté des sciences de Toulouse Mathématiques 18.2 (2009): 397-443. <http://eudml.org/doc/10112>.

@article{Fornet2009,

abstract = {We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface $\lbrace x_d=0\rbrace .$ Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is $\mathbb\{D\}_t+a(x)\mathbb\{D\}_x,$ with $sign(x a(x))>0$ (expansive case not included in our first result), thus resulting in an infinity of weak solutions. Proving that this problem is uniformly Evans-stable, we show that our viscous approach successfully singles out a solution. Both results are new and incorporates a stability result as well as an asymptotic analysis of the convergence at any order, which results in an accurate boundary layer analysis.},

affiliation = {LATP, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France LMRS, Université de Rouen, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray, France},

author = {Fornet, Bruno},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {small viscosity solutions; geometric stability assumption; boundary layer analysis},

language = {eng},

month = {1},

number = {2},

pages = {397-443},

publisher = {Université Paul Sabatier, Toulouse},

title = {Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients},

url = {http://eudml.org/doc/10112},

volume = {18},

year = {2009},

}

TY - JOUR

AU - Fornet, Bruno

TI - Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2009/1//

PB - Université Paul Sabatier, Toulouse

VL - 18

IS - 2

SP - 397

EP - 443

AB - We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface $\lbrace x_d=0\rbrace .$ Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is $\mathbb{D}_t+a(x)\mathbb{D}_x,$ with $sign(x a(x))>0$ (expansive case not included in our first result), thus resulting in an infinity of weak solutions. Proving that this problem is uniformly Evans-stable, we show that our viscous approach successfully singles out a solution. Both results are new and incorporates a stability result as well as an asymptotic analysis of the convergence at any order, which results in an accurate boundary layer analysis.

LA - eng

KW - small viscosity solutions; geometric stability assumption; boundary layer analysis

UR - http://eudml.org/doc/10112

ER -

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