Stability and total variation estimates on general scalar balance laws

Communications in Mathematical Sciences

Volumn 7, Issue 1, 2009, Pages 37-65

  Colombo, Rinaldo M ^a   Mercier, Magali ^a,b   Rosini, Massimiliano D ^a,c  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITÉ LYON 1   (France)

^c INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Kr zkov entropy solutions; Multi dimensional scalar conservation laws

Indexed keywords

EID: 64549106583     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2009.v7.n1.a2     Document Type: Article

References (18)

1. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 2000.
2. S. Bianchini and R.M. Colombo, On the stability of the standard Riemann semigroup, Proc. Amer. Math. Soc., 130(7), 1961-1973, (electronic), 2002.
3. F. Bouchut and B. Perthame, Kružkov's estimates for scalar conservation laws revisited, Trans. Amer. Math. Soc., 350(7), 2847-2870, 1998.
4. G.Q. Chen and K.H. Karlsen, Quasilinear anisotropic degenerate parabolic equations with time-space dependent diffusion coefficients, Commun. Pure Appl. Anal., 4(2), 241-266, 2005.
5. R.M. Colombo and G. Guerra, Hyperbolic balance laws with a non local source, Commun. Part. Differ. Eqs., 32(12), 1917-1939, 2007.
6. C.M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38, 33-41, 1972.
7. C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, second edition, 325, 2005.
8. M. Di Francesco, Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables, NoDEA, 13(5-6), 531-562, 2007.
9. K.H. Karlsen and N.H. Risebro, On the uniqueness and stability of entropy solutions of non-linear degenerate parabolic equations with rough coefficients, Discrete Contin. Dyn. Syst., 9(5), 1081-1104, 2003.
10. S. Kawashima and S. Nishibata, Cauchy problem for a model system of the radiating gas: weak solutions with a jump and classical solutions, Math. Models Methods Appl. Sci., 9(1), 69-91, 1999.
11. S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, SIAM J. Math. Anal., 30(1), 95-117, (electronic), 1999.
12. S.N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81(123), 228-255, 1970.
13. C. Lattanzio and P. Marcati, Global well-posedness and relaxation limits of a model for radiating gas, J. Differ. Eqs., 190(2), 439-465, 2003.
14. C. Lin, J.F. Coulombel and T. Goudon, Shock profiles for non-equilibrium radiating gases, Phys. D, 218(1), 83-94, 2006.
15. H. Liu and E. Tadmor, Critical thresholds in a convolution model for nonlinear conservation laws, SIAM J. Math. Anal., 33(4), 930-945, (electronic), 2001.
16. B.J. Lucier, A moving mesh numerical method for hyperbolic conservation laws, Math. Comp., 46(173), 59-69, 1986.
17. 1-stability of constants in a model for radiating gases, Commun. Math. Sci., 1(1), 197-205, 2003.
18. A.I. Vol'pert and S.I. Hudjaev, Analysis in classes of discontinuous functions and equations of mathematical physics, Mechanics Analysis, Martinus Nijhoff Publishers, Dordrecht, 8, 1985.