Examples of optimal solutions of infinite horizon variational problems arising in continuum mechanics

2009 ◽  
pp. 159-174
Author(s):  
Alexander Zaslavski
Keyword(s):  
Continuum Mechanics ◽  
Infinite Horizon ◽  
Variational Problems ◽  
Optimal Solutions

scholarly journals Existence and uniform boundedness of optimal solutions of variational problems

1998 ◽  
Vol 3 (3-4) ◽  
pp. 265-292 ◽  
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Minimization Problem ◽  
Infinite Horizon ◽  
Uniform Boundedness ◽  
Approximate Solutions ◽  
Variational Problems ◽  
Initial Condition ◽  
Optimal Solutions ◽  
Initial Value ◽  
Horizon Problem ◽  
Bounded Set

Given anx0∈Rnwe study the infinite horizon problem of minimizing the expression∫0Tf(t,x(t),x′(t))dtasTgrows to infinity wherex:[0,∞)→Rnsatisfies the initial conditionx(0)=x0. We analyse the existence and the properties of approximate solutions for every prescribed initial valuex0. We also establish that for every bounded setE⊂RntheC([0,T])norms of approximate solutionsx:[0,T]→Rnfor the minimization problem on an interval[0,T]withx(0),x(T)∈Eare bounded by some constant which does not depend onT.

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