HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS FOR THE DESCRIPTION OF MASS-LESS PARTICLES

TitleHYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS FOR THE DESCRIPTION OF MASS-LESS PARTICLES
Publication TypeJournal Article
Year of Publication2017
AuthorsPENNISI, SEBASTIANO
Volume21
Issue3
Start Page353
Pagination24
Date Published04/2017
Type of Workscientific: mathematics
ISSN1083-2564
AMS35Lxx
Abstract

Hyperbolic systems of partial differential equations are very important for physical applications because they satisfy the causality principle and lead to finite propagation of shocks waves. Many of this cases have been considered in Extended Thermodynamics. Here a new example of physical application is obtained by applying the new theory of the two blocks of balance equations to the case of mass-less particles, in the relativistic
context.
URLhttp://www.acadsol.eu/en/articles/21/3/3.pdf
DOI10.12732/caa.v21i3.2
Short TitleHyperbolic Partial Differential Equations
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

REFERENCES 

[1] I-S. Liu, I. Müller, Extended Thermodynamics of Classical and Degenerate Ideal Gases Arch. Rat. Mech. Anal., 83 (1983), 285-332, doi: 10.1007/BF00963838. 

[2] I. M¨uller, T. Ruggeri, Rational Extended Thermodynamics, 2nd edn. Springer Tracts in Natural Philosophy. Springer, New York (1998), doi: 10.1007/978-1-4612-2210-1. 

[3] M.C. Carrisi, S. Montisci, S. Pennisi, Entropy principle and galilean relativity for dense gases, the general solution without approximations Entropy, 15 (2013), 1035-1056, doi: 10.3390/e15031035. 

[4] M.C. Carrisi, S. Pennisi, An 18 moments model for dense gases: Entropy and Galilean Relativity Principles without expansions, Entropy, 817 (2015), 214-230,, doi: 10.3390/e17010214. 

[5] M.C. Carrisi, S., Pennisi, T. Ruggeri, The Lagrangian view-point xompared with the Eulerian one, in the framework of Extended Thermodynamics, Acta Appl. Math., 132 (2014), 199-212, doi: 10.1007/s10440-0149921-0. 

[6] I.S. Liu, I. M¨uller, T. Ruggeri, Relativistic thermodynamics of gases, Ann. Phys. (N.Y.), 169 (1986), 191-219, doi: 10.1016/0003-4916(86)90164-8. 

[7] M.C. Carrisi, S. Pennisi, Extended Thermodynamics of Charged Gases with Many Moments: An Alternative Closure, J. Math. Phys., 54 (9) (2013), 09301:1-15, doi: 10.1063/1.4821086. 

[8] M.C. Carrisi, A. Farci, M. Obounou, S. Pennisi, Relativistic Extended Thermodynamics from the Lagrangian view-point Ricerche di Matematica, 64 (2015), 357-376, doi: 10.1007/s11587-015-0244-x. 

[9] I-S. Liu, Method of Lagrange Multipliers for Exploitation of the Entropy Principle, Arch. Rat. Mech. Anal., 46 (1972), 131-148, doi: 10.1007/BF00250688. 374 S. Pennisi 

[10] T. Ruggeri, A. Strumia, Main Field and Convex Covariant Density for Quasi-Linear Hyperbolic Systems. Relativistic Fluid Dynamics, Ann. Inst. H. Poincar´e , 34 (1981), 65-84. 

[11] A. Strumia, Wave propagation and symmetric hyperbolic systems of conservation laws with constrained field varaibles. II. Symmetric hyperbolic systems with constrained fields, Nuov Cim B., 101 (1988), 19-37, doi: 10.1007/BF02828067. 

[12] T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended Thermodynamics of dense gases, Continuum Mech. Thermodyn., 24 (2012), 271-292, doi: 10.1007/s00161-011-0213-x. 

[13] T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended Thermodynamics of real gases with dynamic pressure: An extension of Meixner’s theory, Physics Letters A., 376 (2012), 2799-2803, doi: 10.1016/j.physleta.2012.08.030. 

[14] T. Arima, A. Mentrelli, T. Ruggeri, Molecular Extended Thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments, Ann. Phys., 345 (2014), 111-132, doi: 10.1016/j.aop.2014.03.011. 

[15] T. Ruggeri, M. Sugiyama, Rational Extended Thermodynamics beyond the Monatomic Gas, Springer Verlag (2015), doi: 10.1007/978-3-319-13341-6. 

[16] M.C. Carrisi, S. Pennisi, T. Ruggeri, M. Sugiyama, Extended thermodynamics of dense gases in the presence of dynamic pressure, Ricerche di Matematica, 64 (2015), 403-419, doi: 10.1007/s11587-015-0247-7. 

[17] M.C. Carrisi, S. Pennisi, Extended thermodynamics for dense gases up to whatever order, Int. Journal of Non-Linear Mech. , 77 (2015), 74-84, doi: 10.1016/ijnonlinmec.2015.07.011. 

[18] M.C. Carrisi, R. E. Tchame, M.Obounou, S. Pennisi, Extended Thermodynamics for dense gases up to whatever order and with only some symmetries, Entropy , 17 (2015), 7052-7075, doi: 10.3390/e17107052. HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS... 375 

[19] M.C. Carrisi, S. Pennisi, J.M. Sellier, Extended thermodynamics of dense gases with at least 24 moments, Ricerche di Matematica, 65 (2016), 505522, doi: 10.1007/s11587-016-0271-2. 

[20] M.C. Carrisi, S. Pennisi, J.M. Sellier, Extended thermodynamics of dense gases with many moments - The macroscopic approach, Int. Journal of Non-Linear Mech. , 84 (2016), 12-22, doi: 10.1016/j.ijnonlinmec.20156.04.003. 

[21] M.C. Carrisi, R. E. Tchame, M. Obounou, S. Pennisi, An exact solution for the macroscopic approach to Extended thermodynamics of dense gases with many moments, IJPAM, 106 (2016), 171-189, doi: 10.12732/ijpam. v106i1.13. 

[22] M.C. Carrisi, S. Pennisi, J.M. Sellier, A kinetic type exact solution for Extended Thermodynamics of dense gases with many moments, Journal of computational and theoretical transport , 45 (2016), No. 3, 162-173, doi: 10.1080/23324309.2016.1149079. 

[23] M.C. Carrisi, R. E. Tchame, M. Obounou, S. Pennisi, A numberable set of exact solutions for the macroscopic approach to Extended thermodynamics of polyatomic gases with many moments, Advances in Mathematical Physics, 2016 (2016), 1-8, doi: 10.1155/2016/1307813. 

[24] M.C. Carrisi, R. Enoh Tchame, M. Obounou, S. Pennisi, The general exact solution for the many moments macroscopic approach to Extended thermodynamics of polyatomic gases, IJPAM, 112 (2017), No. 4, 827-849, doi: 10.12732/ijpam.v112i4.13. 

[25] S. Pennisi, T. Ruggeri, Relativistic Eextended thermodynamics of rarefied polyatomic gas, Annals of Physics, 377 (2017), 414-445, doi: 10.1016/j.aop.2016.12.012. 

[26] S. Pennisi, Extended Thermodynamics of Nondegenerate Ultrarelativistic Gases, IL NUOVO CIMENTO B, 104 (1989), 273-290, doi: 10.1007/BF02728402. 

[27] F. Borghero, F. Demontis, S. Pennisi, An Exact Macroscopic Model 376 S. Pennisi with Many Moments for Ultrarelativistic Gases, Proceedings of WASCOM 2003, World scientific, Singapore (2004), 94-101. 

[28] F. Borghero, S. Pennisi, The Nonlinear Macroscopic Model of Relaticistic Extended Thermodynamics of an Ultrarelativistic Gas, Rend. Mat. Acc. Lincei, 9 (2004), 59-68. 

[29] F. Demontis, S. Pennisi, On a Further Condition in the Macroscopic Extended Model for Ultrarelativistic Gases, Annali dell’ Universit di Ferrara, 53 (2007), 51-64, doi: 10.1007/s11565-007-0005-1. 

[30] F. Borghero, F. Demontis, S. Pennisi, On the Hyperbolicity of a 30 moments Model for Ultrarelativistic Gases, Meccanica, 48 (2013), 585-600, doi: 10.1007/s11012-012-9617-3. 

[31] F. Borghero, F. Demontis, S. Pennisi, Wave speeds in the Macroscopic Extended Model for Ultrarelativistic Gases, J. Math. Phys., 54 (2013), 113101-1 to 113101-15, doi: 10.1063/1.4829365. 

[32] S. Pennisi, M. Trovato, Mathematical Characterization of Functions Underlying the Principle of Relativity, LE MATEMATICHE, 44 (1989), 173-204. 

[33] S. Pennisi, On Third order Tensor-valued Isotropic Functions, Int. J. Engng Sci., 30 (1992), 679-692, doi: 10.116/0020-7225(92)90011-5.