
Previous Article
New bounds for eigenvalues of strictly diagonally dominant tensors
 NACO Home
 This Issue

Next Article
An integrated inventory model with variable holding cost under two levels of tradecredit policy
An optimal control problem by parabolic equation with boundary smooth control and an integral constraint
Institute of Mathematics, Economics and Computer Science, Irkutsk State University, Irkutsk, Russia 
In the paper, we consider an optimal control problem by differential boundary condition of parabolic equation. We study this problem in the class of smooth controls satisfying certain integral constraints. For the problem under consideration we obtain a necessary optimality condition and propose a method for improving admissible controls. For illustration, we solve one numerical example to show the effectiveness of the proposed method.
References:
show all references
References:
[1] 
Vladimir Srochko, Vladimir Antonik, Elena Aksenyushkina. Sufficient optimality conditions for extremal controls based on functional increment formulas. Numerical Algebra, Control and Optimization, 2017, 7 (2) : 191199. doi: 10.3934/naco.2017013 
[2] 
Franck Boyer, Víctor HernándezSantamaría, Luz De Teresa. Insensitizing controls for a semilinear parabolic equation: A numerical approach. Mathematical Control and Related Fields, 2019, 9 (1) : 117158. doi: 10.3934/mcrf.2019007 
[3] 
Gaoxi Li, Zhongping Wan, Jiawei Chen, Xiaoke Zhao. Necessary optimality condition for trilevel optimization problem. Journal of Industrial and Management Optimization, 2020, 16 (1) : 5570. doi: 10.3934/jimo.2018140 
[4] 
Sylvain Ervedoza, Enrique Zuazua. A systematic method for building smooth controls for smooth data. Discrete and Continuous Dynamical Systems  B, 2010, 14 (4) : 13751401. doi: 10.3934/dcdsb.2010.14.1375 
[5] 
Peter Giesl. Necessary condition for the basin of attraction of a periodic orbit in nonsmooth periodic systems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 355373. doi: 10.3934/dcds.2007.18.355 
[6] 
R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 497506. doi: 10.3934/dcds.1998.4.497 
[7] 
Dariusz Idczak, Stanisław Walczak. Necessary optimality conditions for an integrodifferential Bolza problem via DubovitskiiMilyutin method. Discrete and Continuous Dynamical Systems  B, 2019, 24 (5) : 22812292. doi: 10.3934/dcdsb.2019095 
[8] 
G. Acosta, Julián Fernández Bonder, P. Groisman, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete and Continuous Dynamical Systems  B, 2002, 2 (2) : 279294. doi: 10.3934/dcdsb.2002.2.279 
[9] 
Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slowfast dynamics. Discrete and Continuous Dynamical Systems  B, 2018, 23 (7) : 29352950. doi: 10.3934/dcdsb.2018112 
[10] 
Piernicola Bettiol, Nathalie Khalil. Necessary optimality conditions for average cost minimization problems. Discrete and Continuous Dynamical Systems  B, 2019, 24 (5) : 20932124. doi: 10.3934/dcdsb.2019086 
[11] 
Shahlar F. Maharramov. Necessary optimality conditions for switching control problems. Journal of Industrial and Management Optimization, 2010, 6 (1) : 4755. doi: 10.3934/jimo.2010.6.47 
[12] 
Karl Kunisch, Lijuan Wang. Bangbang property of time optimal controls of semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 279302. doi: 10.3934/dcds.2016.36.279 
[13] 
U. Biccari, V. HernándezSantamaría, J. Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation. Mathematical Control and Related Fields, 2022, 12 (2) : 495530. doi: 10.3934/mcrf.2021032 
[14] 
Minoru Murai, Kunimochi Sakamoto, Shoji Yotsutani. Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition. Conference Publications, 2015, 2015 (special) : 878900. doi: 10.3934/proc.2015.0878 
[15] 
Sebastian Engel, Karl Kunisch. Optimal control of the linear wave equation by timedepending BVcontrols: A semismooth Newton approach. Mathematical Control and Related Fields, 2020, 10 (3) : 591622. doi: 10.3934/mcrf.2020012 
[16] 
Kerem Uǧurlu. Continuity of cost functional and optimal feedback controls for the stochastic Navier Stokes equation in 2D. Communications on Pure and Applied Analysis, 2017, 16 (1) : 189208. doi: 10.3934/cpaa.2017009 
[17] 
Zhenghuan Gao, Peihe Wang. Global $ C^2 $estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 12011223. doi: 10.3934/dcds.2021152 
[18] 
Liangquan Zhang, Qing Zhou, Juan Yang. Necessary condition for optimal control of doubly stochastic systems. Mathematical Control and Related Fields, 2020, 10 (2) : 379403. doi: 10.3934/mcrf.2020002 
[19] 
JongShenq Guo. Blowup behavior for a quasilinear parabolic equation with nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 7184. doi: 10.3934/dcds.2007.18.71 
[20] 
Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 417437. doi: 10.3934/dcds.2011.29.417 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]