A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy
Alice Fiaschi
SISSA, Via Beirut 2-4, 34014 Trieste, Italy
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Abstract
We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we compare this solution with the one obtained with global minimization.
Cite this article
Alice Fiaschi, A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, pp. 1055–1080
DOI 10.1016/J.ANIHPC.2008.02.003