Discontinuous travelling wave solutions for a class of dissipative hyperbolic models
- Volume: 16, Issue: 1, page 61-71
- ISSN: 1120-6330
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topCurrò, Carmela, and Fusco, Domenico. "Discontinuous travelling wave solutions for a class of dissipative hyperbolic models." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.1 (2005): 61-71. <http://eudml.org/doc/252454>.
@article{Currò2005,
abstract = {Discontinuous shock structure solutions for a general system of balance laws is considered in order to investigate the problem of connecting two equilibrium states lying on different sides of a singular barrier representing a locus of irregular singular points for travelling waves. Within such a theoretical setting a governing system of monoatomic gas is considered.},
author = {Currò, Carmela, Fusco, Domenico},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Shocks; Singular phase plane; Travelling waves; shocks; singular phase plane; travelling waves},
language = {eng},
month = {3},
number = {1},
pages = {61-71},
publisher = {Accademia Nazionale dei Lincei},
title = {Discontinuous travelling wave solutions for a class of dissipative hyperbolic models},
url = {http://eudml.org/doc/252454},
volume = {16},
year = {2005},
}
TY - JOUR
AU - Currò, Carmela
AU - Fusco, Domenico
TI - Discontinuous travelling wave solutions for a class of dissipative hyperbolic models
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/3//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 1
SP - 61
EP - 71
AB - Discontinuous shock structure solutions for a general system of balance laws is considered in order to investigate the problem of connecting two equilibrium states lying on different sides of a singular barrier representing a locus of irregular singular points for travelling waves. Within such a theoretical setting a governing system of monoatomic gas is considered.
LA - eng
KW - Shocks; Singular phase plane; Travelling waves; shocks; singular phase plane; travelling waves
UR - http://eudml.org/doc/252454
ER -
References
top- MÜLLER, I. - RUGGERI, T., Extended Thermodynamics. Springer Tracts on Natural Philosophy, 37, Springer-Verlag, New York1993, 231 pp. (Rational Extended Thermodynamics. Springer-Verlag, new edition, 37, 1998, 393 pp.). Zbl0895.00005MR1632151DOI10.1007/978-1-4612-2210-1
- BOILLAT, G. - RUGGERI, T., Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions. Arch. Rat. Mech. Anal., 137, 1997, 304-320. Zbl0878.35070MR1463797DOI10.1007/s002050050030
- GODUNOV, S.K., An interesting class of quasilinear systems. Sov. Math., 2, 1961, 947-948. Zbl0125.06002MR116141
- FRIEDRICHS, K.O. - LAX, P.D., Systems of conservation equation with a convex extension. Proc. Nat. Acad. Sci. USA, 68, 1971, 1686-1688. Zbl0229.35061MR285799
- BOILLAT, G., Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systémes hyperboliques. C.R. Acad. Sciences Paris, 278 A, 1974, 909-912. Zbl0279.35058MR342870
- BOILLAT, G., Non Linear Fields and Waves. In: T. RUGGERI (ed.), Recent Mathematical Methods in Nonlinear Wave Propagation. CIME Course (Montecatini 1994). Lecture Notes in Mathematics, 1640, Springer-Verlag, 1996, 103-152. Zbl0877.35080MR1600900DOI10.1007/BFb0093705
- RUGGERI, T. - STRUMIA, A., Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics. Ann. Inst. H. Poincaré, 34 A, 1981, 65-84. Zbl0473.76126MR605357
- WHITHAM, G.B., Linear and Nonlinear Waves. J. Wiley-Interscience, New York1974, 636 pp. Zbl0373.76001MR483954
- RUGGERI, T., Breakdown of shock-wave-structure solutions. Phys. Rev., E47(6), 1993, 4135-4140. MR1377905DOI10.1103/PhysRevE.47.4135
- BOILLAT, G. - RUGGERI, T., On the shock structure problem for hyperbolic system of balance laws and convex entropy. Continuum Mech. Thermodyn., 10, 1998, 285-292. Zbl0922.76237MR1652858DOI10.1007/s001610050094
- WEISS, W., Die Berechnung von kontinuierlichen Stofstrukturen in der Kinetischen Gastheorie. Habilitation thesis TU, Berlin1997.
- KAMKE, E., Differentialgleichungen I. Geest & Portig, Leipzig1967. Zbl0194.39301
- BIEBERBACH, L., Theorie der gewohnlichen Differentialgleichungen. Springer-Verlag, Berlin1965, 389 pp. MR176133JFM50.0639.02
- MARCHANT, B.P. - NORBURY, J. - PERUMPANANI, A.J., Traveling shock waves arising in a model of malignant invasion. SIAM J. Appl. Math., 60, 2000, 463-476. Zbl0944.34021MR1740255DOI10.1137/S0036139998328034
- MARCHANT, B.P. - NORBURY, J. - SHERRATT, J.A., Discontinuous travelling wave solutions to a haptotaxis-dominated model of malignant invasion. Nonlinearity, 14, 2001, 1653-1671. Zbl0985.92012MR1867097DOI10.1088/0951-7715/14/6/313
- MARCHANT, B.P. - NORBURY, J., Discontinuous travelling wave solutions for certain hyperbolic systems. IMA J. Appl. Math., 67, 2002, 201-224. Zbl1076.35071MR1897286DOI10.1093/imamat/67.2.201
- PETTET, G.J. - MCELWAIN, D.L.S. - NORBURY, J., Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves. IMA J. Appl. Med. Biol., 17, 2000, 395-413. Zbl0969.92020
- LAX, P.D., Shock Waves and Entropy. In: E. ZARANTONELLO (ed.), Contribution to Non Linear Functional Analysis. Acad. Press, New York1971, 603-634. Zbl0268.35014MR393870
- RUGGERI, T., Shock waves in hyperbolic dissipative systems: non equilibrium gases. In: D. FUSCO - A. JEFFREY (eds.), Euromech colloquium 270 (Reggio Calabria, 25-28 September 1990). Pitman Research Notes in Mathematics, vol. 227, Longman, Harlow1991. Zbl0743.76049
- CURRÓ, C. - FUSCO, D., Shock-like travelling wave solutions for a hyperbolic tumour growth model. In: Proceedings of XII International Conference on Waves and Stability in Continuous Media (Villasimius, Cagliari, June 1-7 2003). World Scientific, 2003, 141-147. Zbl1069.35042MR2089842DOI10.1142/9789812702937_0018
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