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Blow-up of solutions of a nonlinear parabolic equation in damage mechanics

Published online by Cambridge University Press:  09 September 2011

MICHIEL BERTSCH  and
PAOLO BISEGNA
MICHIEL BERTSCH
Affiliation:
Department of Mathematics, University of Rome `Tor Vergata', 00133 Rome, Italy
PAOLO BISEGNA
Affiliation:
Department of Civil Engineering, University of Rome `Tor Vergata', 00133 Rome, Italy
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Abstract

A fully nonlinear, degenerate parabolic equation arising in the theory of damage mechanics is shown to be well-posed. Its solutions blow up in finite time and, under suitable conditions on the initial configuration, the blow-up set, corresponding to the portion of the material which breaks at the blow-up time, is an interval of nonzero measure. In a special but physically relevant case the problem reduces to the study of the blow-up set of solutions of the quasilinear equation

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 1 , February 1997 , pp. 89 - 123
Copyright
1997 Cambridge University Press

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