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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Equipartition of energy for a class of second order equations


Author: David G. Costa
Journal: Proc. Amer. Math. Soc. 64 (1977), 65-70
MSC: Primary 34G05
DOI: https://doi.org/10.1090/S0002-9939-1977-0460830-4
MathSciNet review: 0460830
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Abstract: We consider the Cauchy problem for a class of second order equations of the form $ (d/dt - {A_2})(d/dt - {A_1})u(t) = 0$ in a Hilbert space H. A d'Alembert type solution formula is presented and we give a suitable definition of energy. Also, we derive a necessary and sufficient condition for the asymptotic equipartition of energy (Kinetic and Potential) to hold. These results generalize corresponding results for the abstract wave equation $ ({d^2}/d{t^2} + {A^2})u(t) = 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0460830-4
Article copyright: © Copyright 1977 American Mathematical Society