Existence of Solutions for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions

International Mathematics Research Notices

Volumn , Issue 41, 2003, Pages 2205-2220

  Ambrosio, Luigi ^a   De Lellis, Camille ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141575636     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803131327     Document Type: Article

References (7)

1. L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, preprint, 2003, http://cvgmt.sns.it.
2. A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford Lecture Series in Mathematics and Its Applications, vol. 20, Oxford University Press, Oxford, 2000.
3. _, An ill posed Cauchy problem for a hyperbolic system in two space dimensions, preprint, 2003, http://arxiv.org/abs/math.AP/0302227.
4. C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der Mathematischen Wissenschaften, vol. 325, Springer-Verlag, Berlin, 2000.
5. R. J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), no. 3, 511-547.
6. S. N. Kruzhkov, First order quasilinear equations in several independent variables, Math. USSR-Sb. 10 (1970), 217-243.
7. D. Serre, Systems of Conservation Laws. 2, Geometric Structures, Oscillations, and Initial-Boundary Value Problems, Cambridge University Press, Cambridge, 2000, translated from the 1996 French original by I. N. Sneddon.