The perturbed riemann problem for a balance law

Advances in Differential Equations

Volumn 2, Issue 5, 1997, Pages 779-810

  Mascia, Corrado ^a   Sinestrari, Carlo ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000166143     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. J. Bebernes and D. Eberly, Mathematical problems from combustion theory, Applied Mathematical Sciences vol. 83, Springer-Verlag, New York, 1989.
2. C.M. Dafermos, Characteristics in hyperbolic conservation laws, Nonlinear analysis and mechanics Vol. 1 (Knops R.J., ed.), Research Notes in Math. No. 17, Pitman, Boston, 1977, pp. 1-58.
3. C.M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26 (1977), 1097-1119.
4. A.F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb. 51 (1960), 99-128.
5. H. Fan and J.K. Hale, Large-time behavior in inhomogeneous conservation laws, Arch. Rat. Mech. Anal. 125 (1993), 201-216.
6. E. Godlewski and P. Raviart, Hyperbolic Systems of Conservation Laws, Mathématiques et applicationes, n.3/4, S.M.A.I., Ellipses, Paris, 1991.
7. F.R. Guarguaglini, On a class of balance laws with absorption: support properties and finite time extinction, J. Math. Anal. Appl. 188 (1994), 500-520.
8. F.R. Guarguaglini, Singular solutions and asymptotic behaviour for a class of conservation laws with absorption, Comm. Partial Differential Equations 20 (1995), 1395-1425.
9. L. Hsiao, Hyperbolic systems with dissipation, Qualitative aspects and applications of nonlinear evolution equations (T.T. Li, P. De Mottoni, eds.), World Scientific Publishing, Singapore, 1991, pp. 86-106.
10. S.N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbornik 10 (1970), 217-243.
11. C.Z. Li and T.P. Liu, Asymptotic states for hyperbolic conservation laws with a moving source, Adv. Appl. Math. 4 (1983), 353-379.
12. T.P. Liu, Invariants and asymptotic behavior of solutions of a conservation law, Proc. Amer. Math. Soc. 71 (1978), 227-231.
13. T.P. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28:11 (1987), 2593-2602.
14. A.N. Lyberopoulos, Large time structure of solutions of scalar conservation laws without convexity in the presence of a linear source field, J. Diff. Eq. 99 (1992), 342-380.
15. A.N. Lyberopoulos, A Poincaré-Bendixson theorem for scalar balance laws, Proc. Roy. Soc. Edinburgh 124A (1994), 589-607.
16. C. Mascia, Travelling wave solutions for a balance law, Proc. Roy. Soc. Edinburgh (to appear).
17. J.D. Murray, On the Gunn effect and other physical examples of perturbed conservation equations, J. Fluid Mech. 44 (1970), 315-346.
18. R. Natalini, C. Sinestrari, and A. Tesei, Incomplete blow-up of solutions of quasilinear hyperbolic balance laws, Arch. Rat. Mech. Anal. 135 (1996), 259-296.
19. R. Natalini and A. Tesei, On a class of perturbed conservation laws, Adv. Appl. Math. 13 (1992), 429-453.
20. C. Sinestrari, Large time behaviour of solutions of balance laws with periodic initial data, NoDEA 2 (1995), 111-131.
21. C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, Differential and Integral Equations 9 (1996), 499-525.
22. C. Sinestrari, The Riemann problem for an inhomogeneous conservation law without convexity, SIAM J. Math. Anal. (to appear).
23. C. Sinestrari, Instability of discontinuous travelling waves for hyperbolic conservation laws, J. Differential Equat. (to appear).
24. J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983.