Equipartition of energy for a class of second order equations
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- by David G. Costa PDF
- Proc. Amer. Math. Soc. 64 (1977), 65-70 Request permission
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 $({d^2}/d{t^2} + {A^2})u(t) = 0$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- 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