Construction of entropy solutions for one dimensional elastodynamics via time discretisation |
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| Authors: | Sophia Demoulini David M. A. Stuart Athanasios E. Tzavaras |
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| Affiliation: | a Mathematical Institute, University of Oxford, Oxford, UK;b Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK;c Department of Mathematics, University of Wisconsin-Madison, Wiskonsin, WI, USA |
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| Abstract: | It is shown that the variational approximation scheme for one-dimensional elastodynamics given by time discretisation converges, subsequentially, weakly and a.e. to a weak solution which satisfies the entropy inequalities. We also prove convergence under the restriction of positive spatial derivative (for longitudinal motions). |
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