In this work, we study both minimal and maximal blowup time controls for some ordinary differential equations. The existence and Pontryagin’s maximum principle for these problems are derived. As a key preliminary to prove our main results, due to certain monotonicity of the controlled systems, “the initial period optimality” for an optimal triplet is built up. This property reduces our blowup time optimal control problems (where the target set is outside of the state space) to the classical ones (where the target sets are in state spaces).
DOI : 10.1051/cocv/2014051
Mots-clés : Optimal blowup time, initial period optimality, existence, maximum principle
@article{COCV_2015__21_3_815_0,
author = {Lou, Hongwei and Wang, Weihan},
title = {Optimal blowup time for controlled ordinary differential equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {815--834},
publisher = {EDP-Sciences},
volume = {21},
number = {3},
year = {2015},
doi = {10.1051/cocv/2014051},
mrnumber = {3358631},
zbl = {1318.49004},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014051/}
}
TY - JOUR AU - Lou, Hongwei AU - Wang, Weihan TI - Optimal blowup time for controlled ordinary differential equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 815 EP - 834 VL - 21 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014051/ DO - 10.1051/cocv/2014051 LA - en ID - COCV_2015__21_3_815_0 ER -
%0 Journal Article %A Lou, Hongwei %A Wang, Weihan %T Optimal blowup time for controlled ordinary differential equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 815-834 %V 21 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014051/ %R 10.1051/cocv/2014051 %G en %F COCV_2015__21_3_815_0
Lou, Hongwei; Wang, Weihan. Optimal blowup time for controlled ordinary differential equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 815-834. doi : 10.1051/cocv/2014051. http://www.numdam.org/articles/10.1051/cocv/2014051/
and , Blowup in diffusion equations: a survey. J. Comput. Appl. Math. 97 (1998) 3–22. | DOI | MR | Zbl
and , Optimal control of the blowup time. SIAM J. Control Optim. 34 (1996) 102–123. | DOI | MR | Zbl
and , Boundedness and blow up for a semilinear reaction diffusion system. J. Differ. Equ. 89 (1991) 176–202. | DOI | MR | Zbl
, On certain questions in the theory of optimal control. SIAM J. Control Ser. A 1 (1962) 76–84. | MR | Zbl
, Blow-up theorems for nonlinear wave-equations. Mathematische Zeitschrift 132 (1973) 183–203. | DOI | MR | Zbl
and , Blowup rate for heat equation in Lipschitz domains with nonlinear heat source terms on the boundary. J. Math. Anal. Appl. 269 (2002) 28–49. | DOI | MR | Zbl
and , Blowup time optimal control for ordinary differential equations. SIAM J. Control Optim. 49 (2011) 73–105. | DOI | MR | Zbl
, and , Time optimal control problems for some non-smooth systems. Math. Control Relat. Fields 4 (2014) 289–314. | DOI | MR | Zbl
and , Finite-time blowup for wave equations with a potential. SIAM J. Math. Anal. 36 (2005) 1426–1433. | DOI | MR | Zbl
K. Yosida, Functional analysis, 6th ed. Springer-Verlag, Berlin (1980). | MR
and , Rate estimates of gradient blowup for a heat equation with exponential nonlinearity. Nonlin. Anal. Theory Methods Appl. 72 (2010) 4594–4601. | DOI | MR | Zbl
Cité par Sources :
