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The goal of this work is to provide a general framework to study singular limits of initial-value problems for first-order quasilinear hyperbolic systems with stiff source terms in several space variables. We propose structural stability conditions of the problem and construct an approximate solution by a formal asymptotic expansion with initial layer corrections. In general, the equations defining the approximate solution may come together with differential constraints, and so far there are no results for the existence of solutions. Therefore, sufficient conditions are shown so that these equations are parabolic without differential constraint. We justify rigorously the validity of the asymptotic expansion on a time interval independent of the parameter, in the case of the existence of approximate solutions. Applications of the result include Euler equations with damping and an Euler–Maxwell system with relaxation. The latter system was considered in [27,9] which contain ideas used in the present paper.
Keywords: First-order quasilinear hyperbolic system, Singular limit, Structural stability condition, Differential constraint, Parabolic limit equations
@article{AIHPC_2016__33_4_1103_0,
author = {Peng, Yue-Jun and Wasiolek, Victor},
title = {Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1103--1130},
publisher = {Elsevier},
volume = {33},
number = {4},
year = {2016},
doi = {10.1016/j.anihpc.2015.03.006},
zbl = {1347.35023},
mrnumber = {3519534},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.006/}
}
TY - JOUR AU - Peng, Yue-Jun AU - Wasiolek, Victor TI - Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1103 EP - 1130 VL - 33 IS - 4 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.006/ DO - 10.1016/j.anihpc.2015.03.006 LA - en ID - AIHPC_2016__33_4_1103_0 ER -
%0 Journal Article %A Peng, Yue-Jun %A Wasiolek, Victor %T Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1103-1130 %V 33 %N 4 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.006/ %R 10.1016/j.anihpc.2015.03.006 %G en %F AIHPC_2016__33_4_1103_0
Peng, Yue-Jun; Wasiolek, Victor. Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1103-1130. doi: 10.1016/j.anihpc.2015.03.006
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