@article{AIHPC_2003__20_6_975_0, author = {Berthelin, F and Bouchut, F}, title = {Weak solutions for a hyperbolic system with unilateral constraint and mass loss}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {975--997}, publisher = {Elsevier}, volume = {20}, number = {6}, year = {2003}, doi = {10.1016/S0294-1449(03)00012-X}, mrnumber = {2008686}, zbl = {1079.76063}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S0294-1449(03)00012-X/} }
TY - JOUR AU - Berthelin, F AU - Bouchut, F TI - Weak solutions for a hyperbolic system with unilateral constraint and mass loss JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 975 EP - 997 VL - 20 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S0294-1449(03)00012-X/ DO - 10.1016/S0294-1449(03)00012-X LA - en ID - AIHPC_2003__20_6_975_0 ER -
%0 Journal Article %A Berthelin, F %A Bouchut, F %T Weak solutions for a hyperbolic system with unilateral constraint and mass loss %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 975-997 %V 20 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S0294-1449(03)00012-X/ %R 10.1016/S0294-1449(03)00012-X %G en %F AIHPC_2003__20_6_975_0
Berthelin, F; Bouchut, F. Weak solutions for a hyperbolic system with unilateral constraint and mass loss. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 6, pp. 975-997. doi : 10.1016/S0294-1449(03)00012-X. http://archive.numdam.org/articles/10.1016/S0294-1449(03)00012-X/
[1] Problème d'obstacle pour une équation quasi-linéaire du premier ordre, Ann. Fac. Sci. Toulouse Math. 9 (1988) 137-159. | Numdam | MR | Zbl
,[2] Existence and weak stability for a pressureless model with unilateral constraint, Math. Models Methods Appl. Sci. 12 (2002) 249-272. | MR | Zbl
,[3] Solution with finite energy to a BGK system relaxing to isentropic gas dynamics, Ann. Fac. Sci. Toulouse 9 (2000) 605-630. | Numdam | MR | Zbl
, ,[4] Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, Asymptotic Analysis 31 (2002) 153-176. | MR | Zbl
, ,[5] On zero pressure gas dynamics, in: Advances in Kinetic Theory and Computing, Ser. Adv. Math. Appl. Sci., 22, World Scientific, River Edge, NJ, 1994, pp. 171-190. | MR | Zbl
,[6] Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Stat. Phys. 95 (1999) 113-170. | MR | Zbl
,[7] Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Ration. Mech. Anal. 157 (2001) 75-90. | MR | Zbl
,[8] A hierarchy of models for two-phase flows, J. Nonlinear Sci. 10 (2000) 639-660. | MR | Zbl
, , , ,[9] Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness, Comm. Partial Differential Equations 24 (1999) 2173-2189. | MR | Zbl
, ,[10] A solution with bounded expansion rate to the model of viscous pressureless gases, SIAM J. Math. Anal. 32 (2000) 172-193. | MR | Zbl
,[11] A kinetic formulation for multi-branch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 169-190. | Numdam | MR | Zbl
, ,[12] Sticky particles and scalar consevation laws, SIAM J. Numer. Anal. 35 (1998) 2317-2328. | MR | Zbl
, ,[13] B. Després, Equality or convex inequality constraints and hyperbolic systems of conservation laws with entropy, Preprint, 2001.
[14] Lp regularity of velocity averages, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 271-287. | Numdam | MR | Zbl
, , ,[15] Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys. 177 (1996) 349-380. | MR | Zbl
, , ,[16] Une approche analytique d'un modèle black-oil des écoulements triphasiques compressibles en ingénierie pétrolière, J. Mécanique Théor. Appl. 6 (1987) 547-569. | MR | Zbl
, , ,[17] Existence globale pour le système des gaz sans pression, C. R. Acad. Sci. Paris Sér. I Math. 321 (2) (1995) 171-174. | MR | Zbl
,[18] Problèmes unilatéraux pour des équations non linéaires de convection-réaction, Ann. Fac. Sci. Toulouse Math. 4 (1995) 593-631. | Numdam | MR | Zbl
,[19] Obstacle problems for scalar conservation laws, M2AN Math. Model. Numer. Anal. 35 (2001) 575-593. | Numdam | MR | Zbl
,[20] On a free boundary barotropic model, Ann. Inst. H. Poincaré Anal. Non linéaire 16 (1999) 373-410. | Numdam | MR | Zbl
, ,[21] Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 49 (1996) 599-638. | MR | Zbl
, , ,[22] Inéquations variationnelles et quasivariationnelles hyperboliques du premier ordre, J. Math. Pures Appl. (9) 55 (1976) 353-378. | MR | Zbl
, ,[23] A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517. | MR | Zbl
, ,[24] Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, Ann. Inst. H. Poincaré Anal. Non linéaire 17 (2000) 169-192. | Numdam | MR | Zbl
,[25] Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas, SIAM J. Numer. Anal. 36 (1999) 465-474. | MR | Zbl
,[26] Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with γ=3, Indiana Univ. Math. J. 48 (1999) 347-364. | Zbl
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