We establish a necessary and sufficient condition for decay of periodic entropy solutions to a multidimensional conservation law with merely continuous flux vector.
Nous considérons les lois de conservation [hyperboliques] en plusieurs dimensions dʼespace avec la fonction de flux seulement continue. Nous établissons une condition nécessaire et suffisante pour la décroissance des solutions entropiques périodiques de ce problème.
Keywords: Conservation laws, Periodic entropy solutions, Decay property, H-measures
@article{AIHPC_2013__30_6_997_0,
author = {Panov, E.Yu.},
title = {On decay of periodic entropy solutions to a scalar conservation law},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {997--1007},
year = {2013},
publisher = {Elsevier},
volume = {30},
number = {6},
doi = {10.1016/j.anihpc.2012.12.009},
mrnumber = {3132413},
zbl = {1288.35347},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2012.12.009/}
}
TY - JOUR AU - Panov, E.Yu. TI - On decay of periodic entropy solutions to a scalar conservation law JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 997 EP - 1007 VL - 30 IS - 6 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2012.12.009/ DO - 10.1016/j.anihpc.2012.12.009 LA - en ID - AIHPC_2013__30_6_997_0 ER -
%0 Journal Article %A Panov, E.Yu. %T On decay of periodic entropy solutions to a scalar conservation law %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 997-1007 %V 30 %N 6 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2012.12.009/ %R 10.1016/j.anihpc.2012.12.009 %G en %F AIHPC_2013__30_6_997_0
Panov, E.Yu. On decay of periodic entropy solutions to a scalar conservation law. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, pp. 997-1007. doi: 10.1016/j.anihpc.2012.12.009
[1] , , Decay of entropy solutions of nonlinear conservation laws, Arch. Ration. Mech. Anal. 146 no. 2 (1999), 95-127 | MR | Zbl
[2] , Measure-valued solutions to conservation laws, Arch. Ration. Mech. Anal. 88 (1985), 223-270 | MR | Zbl
[3] , Microlocal defect measures, Comm. Partial Differential Equations 16 (1991), 1761-1794 | MR | Zbl
[4] , First order quasilinear equations in several independent variables, Mat. Sb. 81 (1970), 228-255, Math. USSR-Sb. 10 (1970), 217-243 | MR | Zbl
[5] , , First-order conservative quasilinear laws with an infinite domain of dependence on the initial data, Dokl. Akad. Nauk SSSR 314 (1990), 79-84, Soviet Math. Dokl. 42 (1991), 316-321 | MR | Zbl
[6] , , Osgoodʼs type conditions for uniqueness of entropy solutions to Cauchy problem for quasilinear conservation laws of the first order, Ann. Univ. Ferrara Sez. VII (N.S.) 40 (1994), 31-54 | MR | Zbl
[7] , , Renormalized entropy solutions to the Cauchy problem for first order quasilinear conservation laws in the class of periodic functions, J. Math. Sci. 177 no. 1 (2011), 27-49 | MR | Zbl
[8] , On sequences of measure-valued solutions of first-order quasilinear equations, Mat. Sb. 185 no. 2 (1994), 87-106, Russian Acad. Sci. Sb. Math. 81 no. 1 (1995), 211-227 | MR | Zbl
[9] , On strong precompactness of bounded sets of measure valued solutions for a first order quasilinear equation, Mat. Sb. 186 no. 5 (1995), 103-114, Russian Acad. Sci. Sb. Math. 186 no. 5 (1995), 729-740 | MR | Zbl
[10] , Property of strong precompactness for bounded sets of measure valued solutions of a first-order quasilinear equation, Mat. Sb. 190 no. 3 (1999), 109-128, Russian Acad. Sci. Sb. Math. 190 no. 3 (1999), 427-446 | MR | Zbl
[11] , A remark on the theory of generalized entropy sub- and supersolutions of the Cauchy problem for a first-order quasilinear equation, Differ. Uravn. 37 no. 2 (2001), 252-259, Differ. Equ. 37 no. 2 (2001), 272-280 | MR | Zbl
[12] , Maximum and minimum generalized entropy solutions to the Cauchy problem for a first-order quasilinear equation, Mat. Sb. 193 no. 5 (2002), 95-112, Russian Acad. Sci. Sb. Math. 193 no. 5 (2002), 727-743 | MR | Zbl
[13] , Existence of strong traces for generalized solutions of multidimensional scalar conservation laws, J. Hyperbolic Differ. Equ. 2 no. 4 (2005), 885-908 | MR | Zbl
[14] , Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ. 4 no. 4 (2007), 729-770 | MR | Zbl
[15] , Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, Arch. Ration. Mech. Anal. 195 no. 2 (2010), 643-673 | MR | Zbl
[16] , Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics: Heriot. Watt Symposium, vol. 4, Edinburgh, 1979, Res. Notes Math. vol. 39 (1979), 136-212 | MR | Zbl
[17] , H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 115 no. 3–4 (1990), 193-230 | MR | Zbl
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