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Transactions of the American Mathematical Society

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Global existence for a quasi-linear evolution equation with a non-convex energy

Authors: Eduard Feireisl and Hana Petzeltová
Journal: Trans. Amer. Math. Soc. 354 (2002), 1421-1434
MSC (2000): Primary 35Q72, 74D10, 45K05
Published electronically: December 5, 2001
MathSciNet review: 1873012
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Abstract: We establish the existence of global in time weak solutions to the initial-boundary value problem related to the dynamics of coherent solid-solid phase transitions in viscoelasticity. The class of the stored energy functionals includes the double well potential, and a general convolution damping term is considered.

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Additional Information

Eduard Feireisl
Affiliation: Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Hana Petzeltová
Affiliation: Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Received by editor(s): February 19, 2000
Received by editor(s) in revised form: August 29, 2001
Published electronically: December 5, 2001
Additional Notes: Work supported by Grant A1019002 GA AVCR
Article copyright: © Copyright 2001 American Mathematical Society