Theoretical and numerical local null controllability of a quasi-linear parabolic equation in dimensions 2 and 3 |
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| Authors: | E Fernández-Cara J Límaco I Marín-Gayte |
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| Institution: | 1. Dpto. EDAN & IMUS, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain;2. Inst. Matemática - Universidade Federal Fluminense, RJ, Brasil;3. Dpto. EDAN, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain;1. Institute of Automation, Qufu Normal University, Qufu, Shandong 273165, PR China;2. Department of Systems Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan;3. College of Engineering, Qufu Normal University, Rizhao, Shandong 276826, PR China;1. Communication Engineering at Al-Hussein bin Talal University, Ma’an, Jordan;2. Electrical Engineering at Jordan University of Science and Technology, Irbid, Jordan;1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People''s Republic of China;2. College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, People''s Republic of China;1. National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China;2. College of Science, Hohai University, Nanjing 210098, China;3. Department of Electrical Electronics and Telecommunications Engineering, University of Cuenca, Ecuador;4. School of Electrical and Electronic Engineering, University of Adelaide, South Australia 5005, Australia;1. Hangzhou Innovation Institute, Beihang University, 310051, Hangzhou, China;2. School of Automation Science and Electrical Engineering, Beihang University, 100191, China;1. School of Automation, Qingdao University, China;2. Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai, China |
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| Abstract: | This paper is devoted to the theoretical and numerical analysis of the null controllability of a quasi-linear parabolic equation. First, we establish a local controllability result. The proof relies on an appropriate inverse function argument. Then, we formulate an iterative algorithm for the computation of the null control and we prove a convergence result. Finally, we illustrate the analysis with some numerical experiments. |
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