Sistemi iperbolici di leggi di conservazione

 Access to full text

 Full (PDF)

 Full (DjVu)

1. BAITI, P.- JENSSEN, H. K., On the front tracking algorithm, J. Math. Anal. Appl., 217 (1998), 395-404. Zbl0966.35078MR1492096
2. BIANCHINI, S.- BRESSAN, A., BV estimates for a class of viscous hyperbolic systems, Indiana Univ. Math. J., in corso di stampa. 
3. BRESSAN, A., Contractive metrics for nonlinear hyperbolic systems, Indiana Univ. Math. J., 37 (1988), 409-421. Zbl0632.35041MR963510
4. BRESSAN, A., Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl., 170 (1992), 414-432. Zbl0779.35067MR1188562
5. BRESSAN, A., The unique limit of the Glimm scheme, Arch. Rational Mech. Anal., 130 (1995), 205-230. Zbl0835.35088MR1337114
6. BRESSAN, A., Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem, Oxford University Press, 2000. Zbl0997.35002MR1816648
7. BRESSAN, A.- COLOMBO, R. M., The semigroup generated by $2\times 2$ conservation laws, Arch. Rational Mech. Anal., 133 (1995), 1-75. Zbl0849.35068MR1367356
8. BRESSAN, A.- CRASTA, G.- PICCOLI, B., Well posedness of the Cauchy problem for $n\times n$ systems of conservation laws, Amer. Math. Soc. Memoir, 694 (2000). Zbl0958.35001MR1686652
9. BRESSAN, A.- GOATIN, P., Oleinik type estimates and uniqueness for $n\times n$ conservation laws, J. Differential Equations, 156 (1999), 26-49. Zbl0990.35095MR1701818
10. BRESSAN, A.- LEFLOCH, P., Uniqueness of weak solutions to hyperbolic systems of conservation laws, Arch. Rational Mech. Anal., 140 (1997), 301-317. Zbl0903.35039MR1489317
11. BRESSAN, A.- LEWICKA, M., A uniqueness condition for hyperbolic systems of conservation laws, Discr. Cont. Dynam. Syst., in corso di stampa. Zbl1157.35421
12. BRESSAN, A., LIU, T. P. - YANG, T., $L^1$ stability estimates for $n\times n$ conservation laws, Arch. Rational Mech. Anal., 149 (1999), 1-22. Zbl0938.35093MR1723032
13. CRANDALL, M., The semigroup approach to first-order quasilinear equations in several space variables, Israel J. Math., 12 (1972), 108-132. Zbl0246.35018MR316925
14. DAFERMOS, C., Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), 33-41. Zbl0233.35014MR303068
15. DAFERMOS, C., Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, 1999. Zbl0940.35002
16. DIPERNA, R., Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 20 (1976), 187-212. Zbl0314.58010MR404872
17. DIPERNA, R., Entropy and the uniqueness of solutions to hyperbolic conservation laws, in Nonlinear Evolution Equations (M. Crandall Ed.), Academic Press, New York (1978), 1-16. Zbl0469.35064MR513809
18. DIPERNA, R., Uniqueness of solutions to hyperbolic conservation laws, Indiana Univ. Math. J., 28 (1979), 137-188. Zbl0409.35057MR523630
19. DIPERNA, R., Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal., 82 (1983), 27-70. Zbl0519.35054MR684413
20. EVANS, L. C.- GARIEPY, R. F., Measure Theory and Fine Properties of Functions, C.R.C. Press, 1992. Zbl0804.28001MR1158660
21. GLIMM, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), 697-715. Zbl0141.28902MR194770
22. HERRERO, M.- VELAZQUEZ, J., Generic behavior of one-dimensional blow-up patterns, Annali Scuola Norm. Sup. Pisa, Serie IV, 19 (1992), 381-450. Zbl0798.35081MR1205406
23. JENSSEN, H. K., Blowup for systems of conservation laws, SIAM J. Math. Anal., in corso di stampa. Zbl0969.35091MR1752421
24. JOHN, F., Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math., 27 (1974), 377-405. Zbl0302.35064MR369934
25. KRUZHKOV, S., First-order quasilinear equations with several space variables, Math. USSR Sb., 10 (1970), 217-273. Zbl0215.16203
26. LAX, P. D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566. Zbl0081.08803MR93653
27. LEVEQUE, R., Numerical Methods for Conservation Laws, Lecture Notes in Math., Birkhäuser, 1990. Zbl0723.65067MR1077828
28. LIU, T. P., Uniqueness of weak solutions of the Cauchy problem for general $2\times 2$ conservation laws, J. Differential Equations, 20 (1976), 369-388. Zbl0288.76031MR393871
29. LIU, T. P., The deterministic version of the Glimm scheme, Comm. Math. Phys., 57 (1977), 135-148. Zbl0376.35042MR470508
30. LIU, T. P.- YANG, T., $L^1$ stability of conservation laws with coinciding Hugoniot and characteristic curves, Indiana Univ. Math. J., 48 (1999), 237-247. Zbl0935.35090MR1722199
31. LIU, T. P.- YANG, T., $L^1$ stability for $2\times 2$ systems of hyperbolic conservation laws, J. Amer. Math. Soc., 12 (1999), 729-774. Zbl0940.35136MR1646841
32. MAJDA, A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, New York, 1984. Zbl0537.76001MR748308
33. NATALINI, R., Recent results on hyperbolic relaxation problems, in Analysis of Systems of Conservation Laws (H. Freisthüler Ed.), Chapman & Hall/CRC, 1998, pp. 128-198. Zbl0940.35127
34. OLEINIK, O., On the uniqueness of the generalized solution of the Cauchy problem for a nonlinear system of equations occurring in mechanics, Usp. Mat. Nauk., 12, (1957), 169-176. MR94543
35. RAUCH, J., BV estimates fail for most quasilinear hyperbolic systems in dimension greater than one, Comm. Math. Phys., 106 (1986), 481-484. Zbl0619.35073MR859822
36. RISEBRO, N. H., A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc., 117 (1993), 1125-1139. Zbl0799.35153MR1120511
37. SERRE, D., Systémes de Lois de Conservation, Diderot Editeur, 1996. 
38. SMOLLER, J., Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. Zbl0508.35002MR688146
39. VOLPERT, A. I., The spaces BV and quasilinear equations, Math. USSR Sbornik, 2 (1967), 225-267. Zbl0168.07402MR216338