BV solutions and viscosity approximations of rate-independent systems
Alexander Mielke, Riccarda Rossi, Giuseppe Savaré (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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In the nonconvex case, solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity. For the finite-dimensional case we study the vanishing-viscosity limit of doubly nonlinear equations given in terms of a differentiable energy functional and a dissipation potential that is a...