Fine phase mixtures in one-dimensional non-convex elastodynamics

We show that fine phase mixtures arise in the initial-boundary value problem for a class of equations of non-convex elastodynamics in one space dimension. Specifically, we prove that there are infinitely many local-in-time Lipschitz weak solutions to such a problem that exhibit immediate fine-scale oscillations of the strain whenever the range of the initial strain has a nonempty intersection with the elliptic regime. Consequently, such solutions are nowhere C1 in the part of the space-time domain with fine phase mixtures, but are smooth in the other part of the domain. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This article investigates the initial-boundary value problem for a class of equations of non-convex elastodynamics in one space dimension. It is proven that there are infinitely many local-in-time Lipschitz weak solutions to this problem, which exhibit immediate fine-scale oscillations of the strain whenever the range of the initial strain intersects with the elliptic regime. As a result, these solutions are nowhere C1 in the part of the space-time domain with fine phase mixtures, but are smooth in the other part of the domain.