Mathematical Sciences: Mixed-type Problems in Nonlinear Elasticity Related to Change of Phase

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The research project is concerned with an initial- boundary value problem from nonlinear elasticity theory involving nonmonotone stress strain relations. The stable solutions for such a problem will have to minimize a noncovex energy functional. They may exhibit discon- tinuous gradients related to changes of phases. The existence of such stable solutions and their long time limiting behavior will be investigated. The research results will have practical implications in engineering mechanics.