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Hyperbolic Approximation on System of Elasticity in Lagrangian Coordinates
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
Institute of Mathematics, University of Würzburg, Würzburg, Germany
Department of Mathematics, Hangzhou Normal University, Hangzhou, China
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
- 1 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
- 2 Institute of Mathematics, University of Würzburg, Würzburg, Germany
- 3 Department of Mathematics, Hangzhou Normal University, Hangzhou, China
- 4 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
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Abstract
In this paper, we construct a sequence of hyperbolic systems (13) to approximate the general system of one-dimensional nonlinear elasticity in Lagrangian coordinates (2). For each fixed approximation parameter , we establish the existence of entropy solutions for the Cauchy problem (13) with bounded initial data (23).
KeywordsEntropy SolutionsIsentropic Gas DynamicsLax Entropy
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