A Riemann problem for an elastic bar that changes phase

Author:
Yier Lin

Journal:
Quart. Appl. Math. **53** (1995), 575-600

MSC:
Primary 73D35; Secondary 35L67, 35Q72, 73B05, 73C50, 73K05

DOI:
https://doi.org/10.1090/qam/1343469

MathSciNet review:
MR1343469

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Abstract: This paper is concerned with the dynamics of an elastic bar that can undergo reversible stress-induced phase transformations. We consider a Riemann problem in which the initial strains belong to a single metastable phase and prove uniqueness of solution that satisfies a nucleation criterion and a kinetic law at all subsonic and sonic phase boundaries. This paper generalizes the results of [3]; the authors of [3] considered a piecewise-linear material for which no wave fans exist, shock waves always travel at the acoustic speed, and shock waves are dissipation-free. The material model of the present paper does not suffer from these degeneracies.

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DOI:
https://doi.org/10.1090/qam/1343469

Article copyright:
© Copyright 1995
American Mathematical Society