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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:
[1] |
E. N. Barron and W. Liu, Optimal control of the blowup time,, SIAM J. Control Optim., 34 (1996), 102.
doi: 10.1137/S0363012993245021. |
[2] |
S. Kaplan, On the growth of solutions of quasi-linear parabolic equations,, Comm. Pure Appl. Math., 16 (1963), 305.
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 (): 729.
doi: 10.2977/prims/1195191889. |
[4] |
P. Lin, Quenching time optimal control for some ordinary differential equations,, J. Appl. Math., (2014).
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.
doi: 10.1137/090764232. |
[6] |
H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations,, ESAIM: COCV, 21 (2015), 815. Google Scholar |
[7] |
H. Lou, J. Wen and Y. Xu, Time optimal control problems for some non-smooth systems,, Math. Control Relat. Fields, 4 (2014), 289.
doi: 10.3934/mcrf.2014.4.289. |
[8] |
R. Vinter, Optimal Control,, Birkhäuser, (2000).
|
[9] |
J. Warga, Optimal Control of Differential and Functional Equations,, Academic Press, (1972).
|
[10] |
K. Yosida, Functional Analysis,, Springer-Verlag, (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.
doi: 10.1137/S0363012993245021. |
[2] |
S. Kaplan, On the growth of solutions of quasi-linear parabolic equations,, Comm. Pure Appl. Math., 16 (1963), 305.
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 (): 729.
doi: 10.2977/prims/1195191889. |
[4] |
P. Lin, Quenching time optimal control for some ordinary differential equations,, J. Appl. Math., (2014).
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.
doi: 10.1137/090764232. |
[6] |
H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations,, ESAIM: COCV, 21 (2015), 815. Google Scholar |
[7] |
H. Lou, J. Wen and Y. Xu, Time optimal control problems for some non-smooth systems,, Math. Control Relat. Fields, 4 (2014), 289.
doi: 10.3934/mcrf.2014.4.289. |
[8] |
R. Vinter, Optimal Control,, Birkhäuser, (2000).
|
[9] |
J. Warga, Optimal Control of Differential and Functional Equations,, Academic Press, (1972).
|
[10] |
K. Yosida, Functional Analysis,, Springer-Verlag, (1980).
|
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