In this chapter we give a brief account of the variational motion defined by the limit of Euler schemes at vanishing time step. This notion is linked to the study of local minimizers, which provide stationary solutions for such motions, and is a way of defining a gradient flow for smooth energies, but is defined for a wide class of (non-smooth) energies. For the sake of simplicity of exposition, we limit our analysis to a Hilbert setting, even though many results can be proven in general metric spaces. As an example we define a one-dimensional motion for Griffith Fracture energy, that we may compare with the ones obtained as energetic solutions in the quasistatic setting, and as delta-stable evolutions.
KeywordsBoundary Displacement Euler Scheme Variational Motion Give Boundary Condition Vary Boundary Condition
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