[Limites singulières pour le problème de Riemann : diffusion, relaxation et conditions aux limites]
Nous considérons les approximations auto-semblables d'un système hyperbolique non-linéaire à une dimension d'espace avec donnée initiale de type « problème de Riemann », en particulier le système
We consider self-similar approximations of non-linear hyperbolic systems in one space dimension with Riemann initial data, especially the system
Accepté le :
Publié le :
Kayyunnapara T. Joseph 1 ; Philippe G. LeFloch 2
@article{CRMATH_2007__344_1_59_0, author = {Kayyunnapara T. Joseph and Philippe G. LeFloch}, title = {Singular limits for the {Riemann} problem: general diffusion, relaxation, and boundary conditions}, journal = {Comptes Rendus. Math\'ematique}, pages = {59--64}, publisher = {Elsevier}, volume = {344}, number = {1}, year = {2007}, doi = {10.1016/j.crma.2006.11.015}, language = {en}, }
TY - JOUR AU - Kayyunnapara T. Joseph AU - Philippe G. LeFloch TI - Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions JO - Comptes Rendus. Mathématique PY - 2007 SP - 59 EP - 64 VL - 344 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2006.11.015 LA - en ID - CRMATH_2007__344_1_59_0 ER -
%0 Journal Article %A Kayyunnapara T. Joseph %A Philippe G. LeFloch %T Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions %J Comptes Rendus. Mathématique %D 2007 %P 59-64 %V 344 %N 1 %I Elsevier %R 10.1016/j.crma.2006.11.015 %G en %F CRMATH_2007__344_1_59_0
Kayyunnapara T. Joseph; Philippe G. LeFloch. Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 59-64. doi : 10.1016/j.crma.2006.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.015/
[1] Solution of the Riemann problem for a class of hyperbolic conservation laws by the viscosity method, Arch. Rational Mech. Anal., Volume 52 (1973), pp. 1-9
[2] Admissible wave fans in nonlinear hyperbolic systems, Arch. Rational Mech. Anal., Volume 106 (1989), pp. 243-260
[3] Definition and weak stability of nonconservative products, J. Math. Pure Appl., Volume 74 (1995), pp. 483-548
[4] Dynamic flows with liquid/vapor phase transitions, Handbook of Mathematical Fluid Dynamics, vol. I, North-Holland, Amsterdam, 2002, pp. 373-420
[5] Boundary layers in weak solutions to hyperbolic conservation laws, Arch. Rational Mech. Anal., Volume 147 (1999), pp. 47-88
[6] Boundary layers in weak solutions of hyperbolic conservation laws II. Self-similar vanishing diffusion limits, Comm. Pure Appl. Anal., Volume 1 (2002), pp. 51-76
[7] Boundary layers in weak solutions of hyperbolic conservation laws III. Vanishing relaxation limits, Portugal. Math., Volume 59 (2002), pp. 453-494
[8] Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions (O. Rozanova, ed.), Analytical Approaches to Multidimensional Balance Laws, Nova Publishers, 2005
[9] K.T. Joseph, P.G. LeFloch, Singular limits in phase dynamics with physical viscosity and capillarity, Proc. Roy. Soc. Edinburgh Sect. A, in press
[10] P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math. and its Appl., Minneapolis, Preprint # 593, 1989
[11] Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lecture Notes in Mathematics, ETH Zuerich, Birkhäuser, 2002
[12] Existence theory for the Riemann problem for nonconservative hyperbolic systems, C. R. Acad. Sci. Paris Ser. I, Volume 323 (1996), pp. 347-352
[13] A limiting viscosity approach to the Riemann problem for materials exhibiting change of phase, Arch. Rational Mech. Anal., Volume 105 (1989), pp. 327-365
[14] Wave interactions and variation estimates for self-similar viscous limits in systems of conservation laws, Arch. Rational Mech. Anal., Volume 135 (1996), pp. 1-60
- Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure, Networks Heterogeneous Media, Volume 16 (2021) no. 2, p. 283 | DOI:10.3934/nhm.2021007
- Numerical methods with controlled dissipation for small-scale dependent shocks, Acta Numerica, Volume 23 (2014), p. 743 | DOI:10.1017/s0962492914000099
Cité par 2 documents. Sources : Crossref
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier