On the optimization of the initial boundary value problem for a conservation law

Journal of Mathematical Analysis and Applications

Volumn 291, Issue 1, 2004, Pages 82-99

  Colombo, Rinaldo M ^a   Groli, Alessandro ^a  

^a UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Conservation laws; Euler Lagrange equation; Initial boundary value problem

Indexed keywords

EID: 1442331963     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.10.032     Document Type: Article

References (18)

1. F. Ancona, A. Marson, On the attainable set for scalar nonlinear conservation laws with boundary control, SIAM J. Control Optim. 36 (1998) 290-312.
2. F. Ancona, A. Marson, Scalar non-linear conservation laws with integrable boundary data, Nonlinear Anal. 35 (1999) 687-710.
3. C. Bardos, A.Y. le Roux, J.-C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979) 1017-1034.
4. S. Bianchini, On the shift differentiability of the flow generated by a hyperbolic system of conservation laws, Discrete Contin. Dynam. Systems 6 (2000) 329-350.
5. A. Bressan, On the Cauchy problem for systems of conservation laws, in: Actes du 29ème Congrès d'Analyse Numérique: CANum'97 (Larnas, 1997), SMAI, Paris, 1998, pp. 23-36 (electronic).
6. A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford Univ. Press, 2000.
7. A. Bressan, G. Guerra, Shift-differentiability of the flow generated by a conservation law, Discrete Contin. Dynam. Systems 3 (1997) 35-58.
8. A. Bressan, M. Lewicka, Shift differentials of maps in BV spaces, in: M. Grosser, et al. (Eds.), Nonlinear Theory of Generalized Functions, in: Res. Notes Math., vol. 401, Chapman Hall/CRC, 1999, pp. 47-61.
9. A. Bressan, A. Marson, A variational calculus for discontinuous solutions of systems of conservation laws, Comm. Partial Differential Equations 20 (1995) 1491-1552.
10. R.M. Colombo, A. Groli, On the optimization of a conservation law, Calc. Var. Partial Differential Equations, in press.
11. C.M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26 (1977) 1097-1119.
12. C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, first ed., Springer-Verlag, New York, 2000.
13. A.F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, Kluwer Academic, Dordrecht, 1988, transl. from Russian.
14. S.N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.) 81 (1970) 228-255.
15. P. Lefloch, Explicit formula for scalar nonlinear conservation laws with boundary condition, Math. Methods Appl. Sci. 10 (1988) 265-287.
16. T.-T. Li, B.-P. Rao, Exact boundary controllability for quasi-linear hyperbolic systems, SIAM J. Control Optim. 41 (2003) 1748-1755 (electronic).
17. F.-L. Liu, D.L. Russell, Solutions of the Boussinesq equation on a periodic domain, J. Math. Anal. Appl. 194 (1995) 78-102.
18. S. Ulbrich, A sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms, SIAM J. Control Optim. 41 (2002) 740-797 (electronic).