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Analysis and discretization of an optimal control problem for the forced Fisher equation
1. | School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, United States, United States |
2. | Department of Mathematics, Idaho State University, Pocatello, ID 83209, United States |
[1] |
Chunjuan Hou, Yanping Chen, Zuliang Lu. Superconvergence property of finite element methods for parabolic optimal control problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 927-945. doi: 10.3934/jimo.2011.7.927 |
[2] |
Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1641-1670. doi: 10.3934/dcdsb.2010.14.1641 |
[3] |
Runchang Lin, Huiqing Zhu. A discontinuous Galerkin least-squares finite element method for solving Fisher's equation. Conference Publications, 2013, 2013 (special) : 489-497. doi: 10.3934/proc.2013.2013.489 |
[4] |
Jiongmin Yong. Optimality conditions for controls of semilinear evolution systems with mixed constraints. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 371-388. doi: 10.3934/dcds.1995.1.371 |
[5] |
Shakir Sh. Yusubov, Elimhan N. Mahmudov. Optimality conditions of singular controls for systems with Caputo fractional derivatives. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021182 |
[6] |
Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 |
[7] |
Kim Dang Phung, Gengsheng Wang, Xu Zhang. On the existence of time optimal controls for linear evolution equations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 925-941. doi: 10.3934/dcdsb.2007.8.925 |
[8] |
Wolf-Jüergen Beyn, Janosch Rieger. Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 295-312. doi: 10.3934/dcdsb.2013.18.295 |
[9] |
Xiaomeng Li, Qiang Xu, Ailing Zhu. Weak Galerkin mixed finite element methods for parabolic equations with memory. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 513-531. doi: 10.3934/dcdss.2019034 |
[10] |
Qun Lin, Hehu Xie. Recent results on lower bounds of eigenvalue problems by nonconforming finite element methods. Inverse Problems and Imaging, 2013, 7 (3) : 795-811. doi: 10.3934/ipi.2013.7.795 |
[11] |
Zhangxin Chen. On the control volume finite element methods and their applications to multiphase flow. Networks and Heterogeneous Media, 2006, 1 (4) : 689-706. doi: 10.3934/nhm.2006.1.689 |
[12] |
Bin Wang, Lin Mu. Viscosity robust weak Galerkin finite element methods for Stokes problems. Electronic Research Archive, 2021, 29 (1) : 1881-1895. doi: 10.3934/era.2020096 |
[13] |
Jiwei Jia, Young-Ju Lee, Yue Feng, Zichan Wang, Zhongshu Zhao. Hybridized weak Galerkin finite element methods for Brinkman equations. Electronic Research Archive, 2021, 29 (3) : 2489-2516. doi: 10.3934/era.2020126 |
[14] |
Asif Yokus, Mehmet Yavuz. Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2591-2606. doi: 10.3934/dcdss.2020258 |
[15] |
El Hassan Zerrik, Nihale El Boukhari. Optimal bounded controls problem for bilinear systems. Evolution Equations and Control Theory, 2015, 4 (2) : 221-232. doi: 10.3934/eect.2015.4.221 |
[16] |
Philip Trautmann, Boris Vexler, Alexander Zlotnik. Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients. Mathematical Control and Related Fields, 2018, 8 (2) : 411-449. doi: 10.3934/mcrf.2018017 |
[17] |
Bassam Kojok. Global existence for a forced dispersive dissipative equation via the I-method. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1401-1419. doi: 10.3934/cpaa.2009.8.1401 |
[18] |
U. Biccari, V. Hernández-Santamaría, J. Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation. Mathematical Control and Related Fields, 2022, 12 (2) : 495-530. doi: 10.3934/mcrf.2021032 |
[19] |
Dongho Kim, Eun-Jae Park. Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 873-886. doi: 10.3934/dcdsb.2008.10.873 |
[20] |
A. Naga, Z. Zhang. The polynomial-preserving recovery for higher order finite element methods in 2D and 3D. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 769-798. doi: 10.3934/dcdsb.2005.5.769 |
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