@incollection{JEDP_2005____A5_0, author = {Glass, Olivier}, title = {A controllability result for the $1${-D} isentropic {Euler} equation}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {5}, pages = {1--22}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2005}, doi = {10.5802/jedp.18}, mrnumber = {2352774}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.18/} }
TY - JOUR AU - Glass, Olivier TI - A controllability result for the $1$-D isentropic Euler equation JO - Journées équations aux dérivées partielles PY - 2005 SP - 1 EP - 22 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.18/ DO - 10.5802/jedp.18 LA - en ID - JEDP_2005____A5_0 ER -
%0 Journal Article %A Glass, Olivier %T A controllability result for the $1$-D isentropic Euler equation %J Journées équations aux dérivées partielles %D 2005 %P 1-22 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.18/ %R 10.5802/jedp.18 %G en %F JEDP_2005____A5_0
Glass, Olivier. A controllability result for the $1$-D isentropic Euler equation. Journées équations aux dérivées partielles (2005), article no. 5, 22 p. doi : 10.5802/jedp.18. http://www.numdam.org/articles/10.5802/jedp.18/
[1] Alber H.-D., Local existence of weak solutions to the quasilinear wave equation for large initial values. Math. Z. 190 (1985), no. 2, pp. 249–276. | MR | Zbl
[2] Ancona F., Bressan A., Coclite G.M., Some results on the boundary control of systems of conservation laws. Hyperbolic problems: theory, numerics, applications, pp. 255–264, Springer, Berlin, 2003. | MR | Zbl
[3] Ancona F., Coclite G.M., On the attainable set for Temple class systems with boundary controls. Preprint SISSA (2002).
[4] Ancona F., Marson A., On the attainable set for scalar nonlinear conservation laws with boundary control. SIAM J. Control Optim. 36 (1998), no. 1, pp. 290–312. | MR | Zbl
[5] Beauchard K., Local controllability of a -D Schrödinger equation, J. Math. Pures Appl. 84 (2005), no. 7, pp. 851–956. | MR | Zbl
[6] Bressan A., Hyperbolic systems of conservation laws, the one-dimensional problem, Oxford Lecture Series in Mathematics and its Applications 20, 2000. | MR | Zbl
[7] Bressan A., Coclite G.M., On the boundary control of systems of conservation laws. SIAM J. Control Optim. 41 (2002), no. 2, 607–622 | MR | Zbl
[8] Corli A., Sablé-Tougeron M., Perturbations of bounded variation of a strong shock wave. J. Differential Equations 138 (1997), no. 2, pp. 195–228. | MR | Zbl
[9] Coron J.-M., Global Asymptotic Stabilization for controllable systems without drift, Math. Control Signal Systems, 5, 1992, pp. 295-312. | MR | Zbl
[10] Coron J.-M., On the controllability of -D incompressible perfect fluids, J. Math. Pures Appl., 75 (1996), no. 2, pp. 155–188. | MR | Zbl
[11] Coron J.-M. Local controllability of a -D tank containing a fluid modeled by the shallow water equations. A tribute to J. L. Lions. ESAIM Control Optim. Calc. Var. 8 (2002), pp. 513–554. | EuDML | Numdam | MR | Zbl
[12] Dafermos C. M., Polygonal approximations of solutions of the initial value problem for a conservation law. J. Math. Anal. Appl. 38 (1972), pp. 33–41. | MR | Zbl
[13] Di Perna R. J., Global solutions to a class of nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 26 (1973), pp. 1–28. | MR | Zbl
[14] Dubois F., LeFloch P.G., Boundary conditions for nonlinear hyperbolic systems of conservation laws. J. Differential Equations 71 (1988), no. 1, pp. 93–122. | MR | Zbl
[15] Glass O., Exact boundary controllability of Euler equation, ESAIM Control Optim. Calc. Var. 5 (2000) pp. 1–44. | EuDML | Numdam | MR | Zbl
[16] Glass O., On the controllability of the Vlasov-Poisson system. J. Differential Equations 195 (2003), no. 2, pp. 332–379. | MR | Zbl
[17] Glass O., On the controllability of the -D isentropic Euler equation, preprint. | MR
[18] Glimm J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), pp. 697–715. | MR | Zbl
[19] Glimm J., Lax, P. D., Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the A.M.S. 101 (1970). | MR | Zbl
[20] Horsin T., On the controllability of the Burgers equation. ESAIM: Control Opt. Calc. Var. 3 (1998), pp. 83-95. | EuDML | Numdam | MR | Zbl
[21] Lax P. D., Hyperbolic Systems of Conservation Laws. Comm. Pure Appl. Math. 10 (1957), pp. 537-566. | MR | Zbl
[22] Lax P. D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves. CBMS Regional Conference Series in Applied Mathematics, No. 11. SIAM, Philadelphia, 1973. | MR | Zbl
[23] Li T.-T.; Rao B.-P., Exact boundary controllability for quasi-linear hyperbolic systems. SIAM J. Control Optim. 41 (2003), no. 6, pp. 1748–1755. | MR | Zbl
[24] Lions P.-L., Perthame B., Souganidis P. E., Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Comm. Pure Appl. Math. 49 (1996), no. 6, pp. 599–638. | MR | Zbl
[25] Majda A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, New-York, 1984. | MR | Zbl
[26] Risebro, N. H., A front-tracking alternative to the random choice method. Proc. Amer. Math. Soc. 117 (1993), no. 4, pp. 1125–1139. | MR | Zbl
[27] Sablé-Tougeron M., Stabilité de la structure d’une solution de Riemann à deux grands chocs. Ann. Univ. Ferrara Sez. VII (N.S.) 44 (1998), pp. 129–172. | MR | Zbl
[28] Schochet S., Sufficient conditions for local existence via Glimm’s scheme for large BV data. J. Differential Equations 89 (1991), no. 2, 317–354. | MR | Zbl
[29] Wagner D., Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions. J. Differential Equations 68 (1987), no. 1, pp. 118–136. | MR | Zbl
Cité par Sources :