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19.—Concavity and the Evolutionary Properties of a Class of General Materials*

Published online by Cambridge University Press:  14 February 2012

R. N. Hills
Affiliation:
Heriot-Watt University, Edinburgh.
R. J. Knops
Affiliation:
Heriot-Watt University, Edinburgh.

Extract

Concavity arguments have been used by Knops, Levine and Payne [1] to discuss evolutionary properties of weak solutions to an abstract non-linear differential equation in a Hilbert space. These authors demonstrate that provided the non-linearity is suitably restricted and for specified initial data, the norm of the solution becomes unbounded in a finite time. In other words, the solution possesses a finite escape time.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

[1]Knops, R. J., Levine, H. A. and Payne, L. E. 1974. Non-existence, instability and growth theorems for solutions of a class of abstract non-linear equations with applications to nonlinear elastodynamics. Archs Ration. Mech. Analysis, 55, 52.CrossRefGoogle Scholar
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