Abstract
The incompressible limit in nonlinear elasticity is shown to fall under the theory of singular limits of quasilinear symmetric hyperbolic systems developed by Klainerman and Majda. Specifically, initial-value problems for a family of hyperelastic materials with stored energy functions
are considered, whereX andx are reference and deformed coordinates respectively. Under the assumption that the elasticity tensor
is positive definite near the identity matrix and thatw″(1)>0, the following results are proven for appropriate initial data:
i) existence of solutions of the corresponding evolution equations on a time interval independent of λ as λ→∞, and ii) convergence as λ → ∞ of the solutions to a solution of the incompressible elastodynamics equations.
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Communicated by L. Nirenberg
Supported by NSF postdoctoral fellowship #DMS-84-14107
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Schochet, S. The incompressible limit in nonlinear elasticity. Commun.Math. Phys. 102, 207–215 (1985). https://doi.org/10.1007/BF01229377
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DOI: https://doi.org/10.1007/BF01229377