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Mathematics and Mechanics of Solids
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On Uniqueness and Continuous Dependence in the Nonlinear Theory of Mixtures of Elastic Solids with Voids

R. Quintanilla

Matematica Aplicada 2, Universidad Politgcnica de Catalunya, Colom, 11, Terrassa, 08222, Barcelona, Spain

This paper is concerned with static and dynamic deformations in a nonlinear theory of mixtures of elastic materials with voids. First, we extend some conservation laws within the nonlinear theory. A uniqueness result is presented under a condition related to quasi-convexity assumptions in the static problem. The continuous dependence of solutions upon initial state and body forces is established for the dynamical case. A uniqueness result is also presented.

Key Words: elasticity with voids • mixtures • continuous dependence • uniqueness • nonlinear problems

Mathematics and Mechanics of Solids, Vol. 6, No. 3, 281-298 (2001)
DOI: 10.1177/108128650100600305
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