no. 3
Bang-bang property for time optimal control of semilinear heat equation
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 477-499.

This paper studies the bang-bang property for time optimal controls governed by semilinear heat equation in a bounded domain with control acting locally in a subset. Also, we present the null controllability cost for semilinear heat equation and an observability estimate from a positive measurable set in time for the linear heat equation with potential.

DOI : 10.1016/j.anihpc.2013.04.005
Mots clés : Semilinear heat equation, Time optimal control, Bang-bang property, Observability estimate from measurable sets 
@article{AIHPC_2014__31_3_477_0,
     author = {Phung, Kim Dang and Wang, Lijuan and Zhang, Can},
     title = {Bang-bang property for time optimal control of semilinear heat equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {477--499},
     publisher = {Elsevier},
     volume = {31},
     number = {3},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.04.005},
     mrnumber = {3208451},
     zbl = {1295.49005},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.04.005/}
}
TY  - JOUR
AU  - Phung, Kim Dang
AU  - Wang, Lijuan
AU  - Zhang, Can
TI  - Bang-bang property for time optimal control of semilinear heat equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2014
SP  - 477
EP  - 499
VL  - 31
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.04.005/
DO  - 10.1016/j.anihpc.2013.04.005
LA  - en
ID  - AIHPC_2014__31_3_477_0
ER  - 
%0 Journal Article
%A Phung, Kim Dang
%A Wang, Lijuan
%A Zhang, Can
%T Bang-bang property for time optimal control of semilinear heat equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2014
%P 477-499
%V 31
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2013.04.005/
%R 10.1016/j.anihpc.2013.04.005
%G en
%F AIHPC_2014__31_3_477_0
Phung, Kim Dang; Wang, Lijuan; Zhang, Can. Bang-bang property for time optimal control of semilinear heat equation. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 477-499. doi : 10.1016/j.anihpc.2013.04.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.04.005/

[1] J. Apraiz, L. Escauriaza, G. Wang, C. Zhang, Observability inequalities and measurable sets, J. Eur. Math. Soc. (2013) | EuDML | MR | Zbl

[2] S. Anita, D. Tataru, Null controllability for the dissipative semilinear heat equation, Appl. Math. Optim. 46 (2002), 97 -105 | MR | Zbl

[3] V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press, Boston (1993) | MR

[4] T. Duyckaerts, X. Zhang, E. Zuazua, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials, Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008), 1 -41 | EuDML | Numdam | MR | Zbl

[5] L. Escauriaza, F.J. Fernandez, S. Vessella, Doubling properties of caloric functions, Appl. Anal. 85 (2006), 205 -223 | MR | Zbl

[6] H.O. Fattorini, Infinite Dimensional Linear Control Systems: The Time Optimal and Norm Optimal Problems, North-Holland Math. Stud. vol. 201 , Elsevier, Amsterdam (2005) | MR | Zbl

[7] E. Fernández-Cara, S. Guerrero, Global Carleman inequalities for parabolic systems and applications to controllability, SIAM J. Control Optim. 45 (2006), 1399 -1446 | MR | Zbl

[8] E. Fernández-Cara, E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations, Ann. Inst. H. Poincare Anal. Non Lineaire 17 (2000), 583 -616 | EuDML | Numdam | MR | Zbl

[9] K. Kunisch, L. Wang, Time optimal controls of the linear Fitzhugh–Nagumo equation with pointwise control constraints, J. Math. Anal. Appl. 395 (2012), 114 -130 | MR | Zbl

[10] K. Kunisch, L. Wang, Time optimal control of the heat equation with pointwise control constraints, ESAIM Control Optim. Calc. Var. 19 (2013), 460 -485 | EuDML | Numdam | MR | Zbl

[11] J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin (1971) | MR

[12] V. Mizel, T. Seidman, An abstract bang-bang principle and time optimal boundary control of the heat equation, SIAM J. Control Optim. 35 (1997), 1204 -1216 | MR | Zbl

[13] K.D. Phung, G. Wang, Quantitative unique continuation for the semilinear heat equation in a convex domain, J. Funct. Anal. 259 (2010), 1230 -1247 | MR | Zbl

[14] K.D. Phung, G. Wang, An observability estimate for parabolic equations from a measurable set in time and its applications, J. Eur. Math. Soc. 15 (2013), 681 -703 | EuDML | MR | Zbl

[15] G. Wang, The existence of time optimal control of semilinear parabolic equations, Systems Control Lett. 53 (2004), 171 -175 | MR | Zbl

[16] G. Wang, L ∞ -null controllability for the heat equation and its consequences for the time optimal control problem, SIAM J. Control Optim. 47 (2008), 1701 -1720 | MR | Zbl

[17] G. Wang, L. Wang, The bang-bang principle of time optimal controls for the heat equation with internal controls, Systems Control Lett. 56 (2007), 709 -713 | MR | Zbl

Cité par Sources :