In this paper we study the limiting behavior of the value-function for one-dimensional second order variational problems arising in continuum mechanics. The study of this behavior is based on the relation between variational problems on bounded large intervals and a limiting problem on .
Mots clés : Good function, Infinite horizon, Minimal long-run average cost growth rate, Variational problem
@article{AIHPC_2010__27_1_57_0, author = {Zaslavski, Alexander J.}, title = {The limiting behavior of the value-function for variational problems arising in continuum mechanics}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {57--72}, publisher = {Elsevier}, volume = {27}, number = {1}, year = {2010}, doi = {10.1016/j.anihpc.2009.07.005}, zbl = {1181.49003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.07.005/} }
TY - JOUR AU - Zaslavski, Alexander J. TI - The limiting behavior of the value-function for variational problems arising in continuum mechanics JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 57 EP - 72 VL - 27 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.07.005/ DO - 10.1016/j.anihpc.2009.07.005 LA - en ID - AIHPC_2010__27_1_57_0 ER -
%0 Journal Article %A Zaslavski, Alexander J. %T The limiting behavior of the value-function for variational problems arising in continuum mechanics %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 57-72 %V 27 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.07.005/ %R 10.1016/j.anihpc.2009.07.005 %G en %F AIHPC_2010__27_1_57_0
Zaslavski, Alexander J. The limiting behavior of the value-function for variational problems arising in continuum mechanics. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 57-72. doi : 10.1016/j.anihpc.2009.07.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.07.005/
[1] Sobolev Spaces, Academic Press, New York (1975) | Zbl
,[2] The discrete Frenkel–Kontorova model and its extensions I, Phys. D 8 (1983), 381-422 | Zbl
, ,[3] On the value function for nonautonomous optimal control problem with infinite horizon, Systems Control Lett. 56 (2007), 188-196 | Zbl
, , ,[4] Lower semicontinuity of integral functionals, Trans. Amer. Math. Soc. 192 (1974), 51-57 | Zbl
,[5] Optimality in infinite-horizon variational problems under sign conditions, J. Optim. Theory Appl. 106 (2000), 411-419 | Zbl
, ,[6] The value-function of an infinite-horizon linear quadratic problem, Appl. Math. Lett. 16 (2003), 71-78 | Zbl
, ,[7] On the thermodynamics of periodic phases, Arch. Ration. Mech. Anal. 117 (1992), 321-347 | Zbl
, , ,[8] Tracking nonperiodic trajectories with the overtaking criterion, Appl. Math. Optim. 14 (1986), 155-171 | Zbl
,[9] One dimensional infinite horizon variational problems arising in continuum mechanics, Arch. Ration. Mech. Anal. 106 (1989), 161-194 | Zbl
, ,[10] Mathematical Theory of Economic Dynamics and Equilibria, Springer-Verlag, New York (1977) | Zbl
, ,[11] Universal properties of stable states of a free energy model with small parameters, Calc. Var. Partial Differential Equations 6 (1998), 123-142 | Zbl
,[12] On a class of second order variational problems with constraints, Israel J. Math. 111 (1999), 1-28 | Zbl
, ,[13] The structure of extremals of a class of second order variational problems, Ann. Inst. H. Poincaré Anal. Non Linéare 16 (1999), 593-629 | EuDML | Numdam | Zbl
, ,[14] The structure and limiting behavior of locally optimal minimizers, Ann. Inst. H. Poincaré Anal. Non Linéare 19 (2002), 343-370 | EuDML | Numdam | Zbl
, ,[15] Minimax design for a class of distributed parameter systems, Autom. Remote Control 50 (1990), 1333-1340 | Zbl
,[16] Optimization and feedback control of constrained parabolic systems under uncertain perturbations, Optimal Control, Stabilization and Nonsmooth Analysis, Lecture Notes Control Inform. Sci., Springer (2004), 121-132 | Zbl
, ,[17] Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincaré Anal. Non Linéare 3 (1986), 229-272 | EuDML | Numdam | Zbl
,[18] On some results of Moser and of Bangert, Ann. Inst. H. Poincaré Anal. Non Linéare 21 (2004), 673-688 | EuDML | Zbl
, ,[19] On some results of Moser and of Bangert. II, Adv. Nonlinear Stud. 4 (2004), 377-396 | EuDML | Zbl
, ,[20] Ground states in Frenkel–Kontorova model, Math. USSR Izv. 29 (1987), 323-354 | Zbl
,[21] The existence of periodic minimal energy configurations for one-dimensional infinite horizon variational problems arising in continuum mechanics, J. Math. Anal. Appl. 194 (1995), 459-476 | Zbl
,[22] The existence and structure of extremals for a class of second order infinite horizon variational problems, J. Math. Anal. Appl. 194 (1995), 660-696 | Zbl
,[23] Structure of extremals for one-dimensional variational problems arising in continuum mechanics, J. Math. Anal. Appl. 198 (1996), 893-921 | Zbl
,[24] Existence and structure of optimal solutions of variational problems, Proceedings of the Special Session on Optimization and Nonlinear Analysis, Joint AMS-IMU Conference, Jerusalem, May 1995, Contemp. Math. vol. 204 (1997), 247-278 | Zbl
,[25] Turnpike Properties in the Calculus of Variations and Optimal Control, Springer, New York (2006) | Zbl
,[26] On a class of infinite horizon variational problems, Comm. Appl. Nonlinear Anal. 13 (2006), 51-57 | Zbl
,Cité par Sources :