Noether's theorem for higher-order variational problems of Herglotz type

Simão P. S. Santos; Natália Martins; Delfim F. M. Torres

doi:10.3934/proc.2015.990

Article Contents

2015, Volume 2015: 990-999. Doi: 10.3934/proc.2015.990 open access

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Noether's theorem for higher-order variational problems of Herglotz type

1.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro
2.
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro
3.
CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro

Received: August 31, 2014

Revised: June 30, 2015

Published: October 2015

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Abstract

We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler--Lagrange equation, transversality conditions, DuBois--Reymond necessary optimality condition and Noether's theorem for Herglotz's type higher-order variational problems, valid for piecewise smooth functions.

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Mathematics Subject Classification: Primary: 49K15, 49S05; Secondary: 49K05, 34H05.

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References

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