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Optimal blowup/quenching time for controlled autonomous ordinary differential equations
| 1. | School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433 |
| 2. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
References:
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E. N. Barron and W. Liu, Optimal control of the blowup time, SIAM J. Control Optim., 34 (1996), 102-123.
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S. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math., 16 (1963), 305-330.
doi: 10.1002/cpa.3160160307. |
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H. Kawarada, On solutions of initial-boundary problem for $u_t=u_{x x}+1/(1-u)$, Publ. Res. Inst. Math. Sci., 10 (1974/1975), 729-736.
doi: 10.2977/prims/1195191889. |
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P. Lin, Quenching time optimal control for some ordinary differential equations, J. Appl. Math., (2014), Art ID 127809, 13 pp.
doi: 10.1155/2014/127809. |
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P. Lin and G. Wang, Blowup time optimal control for ordinary differential equations, SIAM J. Control Optim., 49 (2011), 73-105.
doi: 10.1137/090764232. |
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H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations, ESAIM: COCV, 21 (2015), 815-834. |
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H. Lou, J. Wen and Y. Xu, Time optimal control problems for some non-smooth systems, Math. Control Relat. Fields, 4 (2014), 289-314.
doi: 10.3934/mcrf.2014.4.289. |
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R. Vinter, Optimal Control, Birkhäuser, Springer, Boston, 2000. |
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J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972. |
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K. Yosida, Functional Analysis, Springer-Verlag, 6th edition, 1980. |
show all references
References:
| [1] |
E. N. Barron and W. Liu, Optimal control of the blowup time, SIAM J. Control Optim., 34 (1996), 102-123.
doi: 10.1137/S0363012993245021. |
| [2] |
S. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math., 16 (1963), 305-330.
doi: 10.1002/cpa.3160160307. |
| [3] |
H. Kawarada, On solutions of initial-boundary problem for $u_t=u_{x x}+1/(1-u)$, Publ. Res. Inst. Math. Sci., 10 (1974/1975), 729-736.
doi: 10.2977/prims/1195191889. |
| [4] |
P. Lin, Quenching time optimal control for some ordinary differential equations, J. Appl. Math., (2014), Art ID 127809, 13 pp.
doi: 10.1155/2014/127809. |
| [5] |
P. Lin and G. Wang, Blowup time optimal control for ordinary differential equations, SIAM J. Control Optim., 49 (2011), 73-105.
doi: 10.1137/090764232. |
| [6] |
H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations, ESAIM: COCV, 21 (2015), 815-834. |
| [7] |
H. Lou, J. Wen and Y. Xu, Time optimal control problems for some non-smooth systems, Math. Control Relat. Fields, 4 (2014), 289-314.
doi: 10.3934/mcrf.2014.4.289. |
| [8] |
R. Vinter, Optimal Control, Birkhäuser, Springer, Boston, 2000. |
| [9] |
J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972. |
| [10] |
K. Yosida, Functional Analysis, Springer-Verlag, 6th edition, 1980. |
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