No Access

ON A CLASS OF HYPERBOLIC BALANCE LAWS

RINALDO M. COLOMBO

Department of Mathematics, University of Brescia, 25133 Brescia, Italy

Search for more papers by this author

and

ANDREA CORLI

Department of Mathematics, University of Ferrara, 44100 Ferrara, Italy

Search for more papers by this author

https://doi.org/10.1142/S0219891604000317Cited by:16 (Source: Crossref)

Abstract

Consider an n×n system of hyperbolic balance laws with coinciding shock and rarefaction curves. This note proves the well-posedness in the large of this system, provided there exists a domain that is invariant both with respect to the homogeneous conservation law and to the ordinary differential system generated by the right-hand side. No "non-resonance" hypothesis is assumed.

Keywords:

AMSC: 35L65, 35L60

References

D. Amadori, L. Gosse and G. Guerra, Arch. Ration. Mech. Anal. 162(4), 327 (2002), DOI: 10.1007/s002050200198. Crossref, Web of Science, Google Scholar
D. Amadori and G. Guerra, Appl. Math. Lett. 12(6), 123 (1999), DOI: 10.1016/S0893-9659(99)00090-7. Crossref, Web of Science, Google Scholar
D. Amadori and G. Guerra, Nonlinear Anal. 49, 987 (2002), DOI: 10.1016/S0362-546X(01)00721-0. Crossref, Web of Science, Google Scholar
P. Bagnerini et al. , Conservation versus balance laws in traffic flow , Proceedings of the Conference Traffic and Granular Flow '03 . Google Scholar
P. Baiti and A. Bressan, Diff. Integral Equations 10(3), 401 (1997). Web of Science, Google Scholar
S. Bianchini, Diff. Integral Equations 13(10–12), 1529 (2000). Google Scholar
A. Bressan , Hyperbolic Systems of Conservation Laws , Oxford Lecture Series in Mathematics and its Applications 20 ( Oxford University Press , Oxford , 2000 ) . Crossref, Google Scholar
A. Bressan and R. M. Colombo, Arch. Ration. Mech. Anal. 133(1), 1 (1995), DOI: 10.1007/BF00375350. Crossref, Web of Science, Google Scholar
A. Bressan and P. Goatin, Diff. Integral Equations 13(10–12), 1503 (2000). Google Scholar
A. Bressan, T.-P. Liu and T. Yang, Arch. Ration. Mech. Anal. 149(1), 1 (1999), DOI: 10.1007/s002050050165. Crossref, Web of Science, Google Scholar
K. N. Chueh, C. C. Conley and J. A. Smoller, Indiana Univ. Math. J. 26(2), 373 (1977), DOI: 10.1512/iumj.1977.26.26029. Crossref, Web of Science, Google Scholar
R. M. Colombo and A. Corli, Semigroup Forum 68(3), 419 (2004). Crossref, Web of Science, Google Scholar
R. M. Colombo and N. H. Risebro, Comm. Partial Differential Equations 23(9–10), 1693 (1998), DOI: 10.1080/03605309808821397. Crossref, Web of Science, Google Scholar
G. Crasta and B. Piccoli, Discrete Contin. Dyn. Syst. 3(4), 477 (1997). Crossref, Web of Science, Google Scholar
C. M. Dafermos , Hyperbolic Conservation Laws in Continuum Physics , 1st edn. ( Springer-Verlag , New York , 2000 ) . Crossref, Google Scholar
C. M. Dafermos and L. Hsiao, Indiana Univ. Math. J. 31(4), 471 (1982), DOI: 10.1512/iumj.1982.31.31039. Crossref, Web of Science, Google Scholar
A. F. Filippov , Differential Equations with Discontinuous Righthand Sides ( Kluwer Academic Publishers Group , Dordrecht , 1988 ) . Crossref, Google Scholar
A. Heibig, Arch. Ration. Mech. Anal. 126(1), 79 (1994), DOI: 10.1007/BF00375697. Crossref, Web of Science, Google Scholar
D. Hoff, Trans. Amer. Math. Soc. 289(2), 591 (1985). Crossref, Web of Science, Google Scholar
A. Levy, Comm. Partial Differential Equations 17(3–4), 657 (1992), DOI: 10.1080/03605309208820858. Crossref, Web of Science, Google Scholar
T. P. Liu, Commun. Math. Phys. 68(2), 141 (1979), DOI: 10.1007/BF01418125. Crossref, Web of Science, Google Scholar
T. Luo and R. Natalini, Proc. Roy. Soc. Edinburgh Sect. A. 128(4), 775 (1998). Crossref, Web of Science, Google Scholar
A. Majda, SIAM J. Appl. Math. 41(1), 70 (1981), DOI: 10.1137/0141006. Crossref, Web of Science, Google Scholar
M. Nagumo, Proc. Phys. — Math. Soc. Japan (3) 24, 551 (1942). Web of Science, Google Scholar
H. K. Rhee , R. Aris and N. R. Amundson , First-Order Partial Differential Equations , Prentice Hall International Series in the Physical and Chemical Engineering Sciences I, II ( Prentice Hall Inc. , Englewood Cliffs, NJ , 1986 ) . Google Scholar
D. Serre, J. Differential Equations 68(2), 137 (1987), DOI: 10.1016/0022-0396(87)90189-6. Crossref, Web of Science, Google Scholar
D. Serre, Richness and the classification of quasilinear hyperbolic systems, in Multidimensional Hyperbolic Problems and Computations (Minneapolis, MN, 1989), Vol. 29 of IMA Vol. Math. Appl. (Springer, New York, 1991), pp. 315–333 . Google Scholar
B. Temple, Trans. Amer. Math. Soc. 280(2), 781 (1983). Crossref, Web of Science, Google Scholar

Vol. 01, No. 04

Metrics

Downloaded 49 times

History

Keywords

PDF download

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

ON A CLASS OF HYPERBOLIC BALANCE LAWS

Abstract

Recommended