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Transactions of the American Mathematical Society

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Young measures and an application of compensated compactness to one-dimensional nonlinear elastodynamics


Author: Peixiong Lin
Journal: Trans. Amer. Math. Soc. 329 (1992), 377-413
MSC: Primary 35L60; Secondary 35A35, 73C50, 73D99
DOI: https://doi.org/10.1090/S0002-9947-1992-1049615-0
MathSciNet review: 1049615
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Abstract: We study the existence problem for the equations of $ 1$-dimensional nonlinear elastodynamics. We obtain the convergence of $ {L^p}(p < \infty )$ bounded approximating sequences generated by the method of vanishing viscosity and the Lax-Friedrichs scheme. The analysis uses Young measures, Lax entropies, and the method of compensated compactness.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1049615-0
Article copyright: © Copyright 1992 American Mathematical Society