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Conservation laws and null divergences

II. Non-negative divergences

Published online by Cambridge University Press:  24 October 2008

Peter J. Olver
Peter J. Olver
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
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Abstract

It is shown that P, depending on x, u and derivatives of u, satisfies Div P ≥ 0 for all such x, u, if and only if Div p = Φ(x) ≥ 0 where Φ is independent of u. Applications to theories of continuum thermomechanics are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 511 - 514
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Anderson, I. M. and Duchamp, T.. On the existence of global variational principles. Amer. J. Math. 102 (1980), 781–868.CrossRefGoogle Scholar
[2]Ball, J. M., Currie, J. C. and Olver, P. J.. Null Lagrangians, weak continuity and variational problems of arbitrary order. J. Funct. Anal. 41 (1981), 135–174.CrossRefGoogle Scholar
[3]Coleman, B. D. and Noll, W.. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13 (1963), 167–178.CrossRefGoogle Scholar
[4]Dunn, J. E.. Interstitial working and a nonclassical continuum thermodynamics. In New Perspectives in Thermodynamics (Springer-Verlag, in the Press).Google Scholar
[5]Dunn, J. E. and Serrin, J.. On the thermomechanics of interstitial working. Arch. Rational Mech. Anal. (in the Press).Google Scholar
[6]Olver, P. J.. Conservation laws and null divergences. Math. Proc. Cambridge Philos. Soc. 94 (1983), 529–540.CrossRefGoogle Scholar