On the piecewise smoothness of entropy solutions to scalar conservation laws

Communications in Partial Differential Equations

Volumn 18, Issue 9-10, 1993, Pages 1631-1652

  Tadmor, Eitan ^a   Tassa, Tamir ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001400260     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605309308820988     Document Type: Article

References (13)

1. Y. Brenier and S. Osher, The discrete one-sided Lipschitz condition for convex scalar conservation laws, SINUM, 25, 1988, 8–23.
2. C.M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 26, 1977, 1097–1119.
3. R. DeVore and B. Lucier, High order regularity for conservation laws, Indiana Univ. Math. J., 39, 1990, 413–430.
4. D. Hoff, The sharp form of Oleinik's entropy condition in several space dimensions, Trans. Amer. Math. Soc., 276, 1983, 527–536.
5. H.O. Kreiss, private communication.
6. P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10, 1957, 537–566.
7. B. Lucier, private communication.
8. O.A. Oleinik, Discontinuous solutions of non-linear differential equations, Amer. Math. Soc. Transl., 26, Ser. 2, 1963, 95–172.
9. O.A. Oleinik, The Cauchy problem for nonlinear equations in a class of discontinuous functions, Amer. Math. Soc. Transl., 42, Ser. 2, 1954, 7–12.
10. O.A. Oleinik, The Cauchy problem for nonlinear differential equations of the first order with discontinuous initial conditions, Trudy Moskov. Mat. Obsc. 5, 1956, 433–454.
11. D.G. Schaeffer, A regularity theorem for conservation laws, Adv. in Math., 11, 1973, 368–386.
12. E. Tadmor, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations, SINUM, 28, No. 4, 1991, 891–906.
13. Z. Xin, Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions, Trans. of AMS, 319, No. 2, 1991, 805–820.