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In this article we construct several important examples of optimal solutions of infinite horizon second order variational problems. The problems are related to a model in thermodynamics introduced in Coleman, Marcus and Mizel, Arch. Rational Mech. Anal. 117 (1992), 321–347.
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Alexander J. Zaslavski, Examples of optimal solutions of infinite horizon variational problems arising in continuum mechanics. Port. Math. 66 (2009), no. 2, pp. 159–174DOI 10.4171/PM/1838