On the attainable set for scalar nonlinear conservation laws with boundary control

SIAM Journal on Control and Optimization

Volumn 36, Issue 1, 1998, Pages 290-312

  Ancona, Fabio ^a   Marson, Andrea ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Attainable set; Boundary control; Conservation laws

Indexed keywords

BOUNDARY VALUE PROBLEMS; SET THEORY; THEOREM PROVING;

BOUNDARY CONTROL; NONLINEAR CONSERVATION LAW;

NONLINEAR CONTROL SYSTEMS;

EID: 0031672504     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996304407     Document Type: Article

References (15)

1. F. ANCONA AND A. MARSON, Scalar Non-linear Conservation Laws with Integrable Boundary Data, Nonlinear Anal., to appear.
2. J. AUBIN AND A. CELLINA, Differential Inclusion, Springer-Verlag, Berlin, New York, 1984.
3. C. BARDOS, A.Y. LEROUX, AND J.C. NEDELEC, First order quasilinear equations with boundary conditions, Comm. in Partial Differential Equations, 9 (1979), pp. 1017-1034.
4. A. BRESSAN, Lectures Notes on Systems of Conservation Laws, S.I.S.S.A., International School for Advanced Studies, Trieste, Italy, 1995.
5. C. DAFERMOS, Generalized characteristic and the structure of solutions of hyperbolic conservation laws, Indiana Math. J., 26 (1977), pp. 1097-1119.
6. F. DUBOIS AND P. LE FLOCH, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 71 (1988), pp. 93-122.
7. A.F. FILIPPOV, Differential equations with discontinuous right-hand side, Amer. Math. Soc. Transl. Ser. 2, 42 (1964), pp. 199-231.
8. A.V. FURSIKOV AND O.YU. IMANUVILOV, Controllability of Evolution Equations, Lecture Notes Series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996.
9. K.E. GUSTAFSON, Partial Differential Equations Second Edition, John Wiley & Sons, New York, 1987.
10. A.D. IOFFE, On lower semicontinuity of integral functional. I, SIAM J. Control Optim., 15 (1977), pp. 521-538.
11. S.N. KRUZKOV, First order quasilinear equations in several independent variables, Math. USSR Sbornik, 10 (1970), pp. 217-243.
12. P.D. LAX, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), pp. 537-566.
13. P.D. LAX, The formation and decay of shock waves, Amer. Math. Monthly, 79 (1972), pp. 227-241.
14. P. LE FLOCH, Explicit formula for scalar non-linear conservation laws with boundary condition, Math. Methods Appl. Sci., 10 (1988), pp. 265-287.
15. J. SMOLLER, Shock Waves and Reaction-Diffusion Equations, 2nd ed., Springer-Verlag, Berlin, New York, 1994.