-
Previous Article
Isogeometric collocation mixed methods for rods
- DCDS-S Home
- This Issue
-
Next Article
Quantum hydrodynamics with nonlinear interactions
The path decomposition technique for systems of hyperbolic conservation laws
1. | Department of Engineering Science, Osaka Electro-Communication University, 18-8 Hatucho, Neyagawa, Osaka 572-8530, Japan |
2. | Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, 44121 Ferrara, Italy |
References:
[1] |
D. Amadori and A. Corli, On a model of multiphase flow, SIAM J. Math. Anal., 40 (2008), 134-166.
doi: 10.1137/07069211X. |
[2] |
D. Amadori and A. Corli, Global existence of BV solutions and relaxation limit for a model of multiphase reactive flow, Nonlinear Anal., 72 (2010), 2527-2541.
doi: 10.1016/j.na.2009.10.048. |
[3] |
D. Amadori and G. Guerra, Global BV solutions and relaxation limit for a system of conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1-26.
doi: 10.1017/S0308210500000767. |
[4] |
F. Asakura, Decay of solutions for the equations of isothermal gas dynamics, Japan J. Indust. Appl. Math., 10 (1993), 133-164.
doi: 10.1007/BF03167207. |
[5] |
F. Asakura, Wave-front tracking for the equations of isentropic gas dynamics, Quart. Appl. Math., 63 (2005), 20-33.
doi: 10.1090/S0033-569X-04-00935-8. |
[6] |
F. Asakura, Wave-front tracking for the equations of non-isentropic gas dynamics-basic lemmas, Acta Math. Vietnam., 38 (2013), 487-516.
doi: 10.1007/s40306-013-0030-3. |
[7] |
F. Asakura and A. Corli, Global existence of solutions by path decomposition for a model of multiphase flow, Quart. Appl. Math., 71 (2013), 135-182.
doi: 10.1090/S0033-569X-2012-01318-4. |
[8] |
F. Asakura and A. Corli, Wave-front tracking for the equations of non-isentropic gas dynamics, Ann. Mat. Pura Appl., 194 (2015), 581-618.
doi: 10.1007/s10231-013-0390-2. |
[9] |
A. Bressan, Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl., 170 (1992), 414-432.
doi: 10.1016/0022-247X(92)90027-B. |
[10] |
A. Bressan, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal., 130 (1995), 205-230.
doi: 10.1007/BF00392027. |
[11] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford University Press, 2000. |
[12] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Third edition, Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04048-1. |
[13] |
R. J. DiPerna, Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 20 (1976), 187-212.
doi: 10.1016/0022-0396(76)90102-9. |
[14] |
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), 697-715.
doi: 10.1002/cpa.3160180408. |
[15] |
S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb. (N.S.), 47 (1959), 271-306. |
[16] |
P. Lax, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), Academic Press, New York, 1971, 603-634. |
[17] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[18] |
T. P. Liu, The deterministic version of the Glimm scheme, Comm. Math. Phys., 57 (1977), 135-148.
doi: 10.1007/BF01625772. |
[19] |
T. P. Liu, Initial-boundary value problems for gas dynamics, Arch. Rational Mech. Anal., 64 (1977), 137-168.
doi: 10.1007/BF00280095. |
[20] |
T. P. Liu, Solutions in the large for the equations of nonisentropic gas dynamics, Indiana Univ. Math. J., 26 (1977), 147-177.
doi: 10.1512/iumj.1977.26.26011. |
[21] |
T. Nishida, Global solution for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Japan Acad., 44 (1968), 642-646.
doi: 10.3792/pja/1195521083. |
[22] |
T. Nishida and J. A. Smoller, Solutions in the large for some nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math., 26 (1973), 183-200.
doi: 10.1002/cpa.3160260205. |
[23] |
N. H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc., 117 (1993), 1125-1139.
doi: 10.1090/S0002-9939-1993-1120511-X. |
[24] |
J. B. Temple, Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics, J. Differential Equations, 41 (1981), 96-161.
doi: 10.1016/0022-0396(81)90055-3. |
[25] |
B. Temple and R. Young, The large time stability of sound waves, Comm. Math. Phys., 179 (1996), 417-466.
doi: 10.1007/BF02102596. |
[26] |
R. Young, Sup-norm stability for Glimm's scheme, Comm. Pure Appl. Math., 46 (1993), 903-948.
doi: 10.1002/cpa.3160460605. |
show all references
References:
[1] |
D. Amadori and A. Corli, On a model of multiphase flow, SIAM J. Math. Anal., 40 (2008), 134-166.
doi: 10.1137/07069211X. |
[2] |
D. Amadori and A. Corli, Global existence of BV solutions and relaxation limit for a model of multiphase reactive flow, Nonlinear Anal., 72 (2010), 2527-2541.
doi: 10.1016/j.na.2009.10.048. |
[3] |
D. Amadori and G. Guerra, Global BV solutions and relaxation limit for a system of conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1-26.
doi: 10.1017/S0308210500000767. |
[4] |
F. Asakura, Decay of solutions for the equations of isothermal gas dynamics, Japan J. Indust. Appl. Math., 10 (1993), 133-164.
doi: 10.1007/BF03167207. |
[5] |
F. Asakura, Wave-front tracking for the equations of isentropic gas dynamics, Quart. Appl. Math., 63 (2005), 20-33.
doi: 10.1090/S0033-569X-04-00935-8. |
[6] |
F. Asakura, Wave-front tracking for the equations of non-isentropic gas dynamics-basic lemmas, Acta Math. Vietnam., 38 (2013), 487-516.
doi: 10.1007/s40306-013-0030-3. |
[7] |
F. Asakura and A. Corli, Global existence of solutions by path decomposition for a model of multiphase flow, Quart. Appl. Math., 71 (2013), 135-182.
doi: 10.1090/S0033-569X-2012-01318-4. |
[8] |
F. Asakura and A. Corli, Wave-front tracking for the equations of non-isentropic gas dynamics, Ann. Mat. Pura Appl., 194 (2015), 581-618.
doi: 10.1007/s10231-013-0390-2. |
[9] |
A. Bressan, Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl., 170 (1992), 414-432.
doi: 10.1016/0022-247X(92)90027-B. |
[10] |
A. Bressan, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal., 130 (1995), 205-230.
doi: 10.1007/BF00392027. |
[11] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford University Press, 2000. |
[12] |
C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Third edition, Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04048-1. |
[13] |
R. J. DiPerna, Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 20 (1976), 187-212.
doi: 10.1016/0022-0396(76)90102-9. |
[14] |
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), 697-715.
doi: 10.1002/cpa.3160180408. |
[15] |
S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb. (N.S.), 47 (1959), 271-306. |
[16] |
P. Lax, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), Academic Press, New York, 1971, 603-634. |
[17] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[18] |
T. P. Liu, The deterministic version of the Glimm scheme, Comm. Math. Phys., 57 (1977), 135-148.
doi: 10.1007/BF01625772. |
[19] |
T. P. Liu, Initial-boundary value problems for gas dynamics, Arch. Rational Mech. Anal., 64 (1977), 137-168.
doi: 10.1007/BF00280095. |
[20] |
T. P. Liu, Solutions in the large for the equations of nonisentropic gas dynamics, Indiana Univ. Math. J., 26 (1977), 147-177.
doi: 10.1512/iumj.1977.26.26011. |
[21] |
T. Nishida, Global solution for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Japan Acad., 44 (1968), 642-646.
doi: 10.3792/pja/1195521083. |
[22] |
T. Nishida and J. A. Smoller, Solutions in the large for some nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math., 26 (1973), 183-200.
doi: 10.1002/cpa.3160260205. |
[23] |
N. H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc., 117 (1993), 1125-1139.
doi: 10.1090/S0002-9939-1993-1120511-X. |
[24] |
J. B. Temple, Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics, J. Differential Equations, 41 (1981), 96-161.
doi: 10.1016/0022-0396(81)90055-3. |
[25] |
B. Temple and R. Young, The large time stability of sound waves, Comm. Math. Phys., 179 (1996), 417-466.
doi: 10.1007/BF02102596. |
[26] |
R. Young, Sup-norm stability for Glimm's scheme, Comm. Pure Appl. Math., 46 (1993), 903-948.
doi: 10.1002/cpa.3160460605. |
[1] |
Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[2] |
Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 597-609. doi: 10.3934/dcds.2006.15.597 |
[3] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[4] |
K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. self-similar vanishing diffusion limits. Communications on Pure and Applied Analysis, 2002, 1 (1) : 51-76. doi: 10.3934/cpaa.2002.1.51 |
[5] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
[6] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
[7] |
Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871 |
[8] |
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control and Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121 |
[9] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
[10] |
Fuqin Sun, Mingxin Wang. Non-existence of global solutions for nonlinear strongly damped hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 949-958. doi: 10.3934/dcds.2005.12.949 |
[11] |
Tong Li, Kun Zhao. Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model. Networks and Heterogeneous Media, 2011, 6 (4) : 625-646. doi: 10.3934/nhm.2011.6.625 |
[12] |
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 717-731. doi: 10.3934/nhm.2007.2.717 |
[13] |
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185 |
[14] |
Paolo Baiti, Helge Kristian Jenssen. Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 837-853. doi: 10.3934/dcds.2001.7.837 |
[15] |
Sachiko Ishida, Tomomi Yokota. Remarks on the global existence of weak solutions to quasilinear degenerate Keller-Segel systems. Conference Publications, 2013, 2013 (special) : 345-354. doi: 10.3934/proc.2013.2013.345 |
[16] |
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks and Heterogeneous Media, 2009, 4 (2) : 393-407. doi: 10.3934/nhm.2009.4.393 |
[17] |
Dmitry V. Zenkov. Linear conservation laws of nonholonomic systems with symmetry. Conference Publications, 2003, 2003 (Special) : 967-976. doi: 10.3934/proc.2003.2003.967 |
[18] |
Valérie Dos Santos, Bernhard Maschke, Yann Le Gorrec. A Hamiltonian perspective to the stabilization of systems of two conservation laws. Networks and Heterogeneous Media, 2009, 4 (2) : 249-266. doi: 10.3934/nhm.2009.4.249 |
[19] |
Zhi-Qiang Shao. Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems of diagonal form with large BV data. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2739-2752. doi: 10.3934/cpaa.2013.12.2739 |
[20] |
C. M. Khalique, G. S. Pai. Conservation laws and invariant solutions for soil water equations. Conference Publications, 2003, 2003 (Special) : 477-481. doi: 10.3934/proc.2003.2003.477 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]