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Optimal control of system governed by the Gao beam equation
1.  Palacký University, Faculty of Science, Department of Mathematical Analysis and Applications of Mathematics, 17. listopadu 1192/12, Olomouc, 771 46, Czech Republic, Czech Republic 
References:
[1] 
A. Borzi, V. Schulz, Computational Optimization of Systems Governed by Partial Differential Equations, SIAM, Philadelphia, 2012. Google Scholar 
[2] 
I. Ekeland, R. Témam, Convex Analysis and Variational Problems, SIAM, Philadelphia, 1999. Google Scholar 
[3] 
D.Y. Gao, Nonlinear elastic beam theory with application in contact problems and variational approaches. Mechanics Research Communications, 23, (1), pp. 1117, 1996. Google Scholar 
[4] 
D.Y. Gao, Finite deformation beam models and triality theory in dynamical postbuckling analysis. Int. J. of NonLinear Mechanics, 35, pp. 103121, 2000. Google Scholar 
[5] 
J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, SpringerVerlag, Berlin, 1971. Google Scholar 
[6] 
J.L. Lions, Some Aspects of the Optimal Control of Distributed Parameter Systems, SIAM, Philadelphia, 1972. Google Scholar 
[7] 
Reddy, J.N.:, An Introduction to the Finite Element Method. Third edition. McGrawHill Book Co., New York, 2006. Google Scholar 
[8] 
F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods and Applications, AMS, Providence, Rhode Island, 2010. Google Scholar 
show all references
References:
[1] 
A. Borzi, V. Schulz, Computational Optimization of Systems Governed by Partial Differential Equations, SIAM, Philadelphia, 2012. Google Scholar 
[2] 
I. Ekeland, R. Témam, Convex Analysis and Variational Problems, SIAM, Philadelphia, 1999. Google Scholar 
[3] 
D.Y. Gao, Nonlinear elastic beam theory with application in contact problems and variational approaches. Mechanics Research Communications, 23, (1), pp. 1117, 1996. Google Scholar 
[4] 
D.Y. Gao, Finite deformation beam models and triality theory in dynamical postbuckling analysis. Int. J. of NonLinear Mechanics, 35, pp. 103121, 2000. Google Scholar 
[5] 
J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, SpringerVerlag, Berlin, 1971. Google Scholar 
[6] 
J.L. Lions, Some Aspects of the Optimal Control of Distributed Parameter Systems, SIAM, Philadelphia, 1972. Google Scholar 
[7] 
Reddy, J.N.:, An Introduction to the Finite Element Method. Third edition. McGrawHill Book Co., New York, 2006. Google Scholar 
[8] 
F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods and Applications, AMS, Providence, Rhode Island, 2010. Google Scholar 
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