Mathematics – Analysis of PDEs
Scientific paper
2009-10-18
Mathematics
Analysis of PDEs
Scientific paper
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 which is a viscous regularization of a given rate-independent dissipation potential. The resulting definition of 'BV solutions' involves, in a nontrivial way, both the rate-independent and the viscous dissipation potential, which play a crucial role in the description of the associated jump trajectories. We shall prove a general convergence result for the time-continuous and for the time-discretized viscous approximations and establish various properties of the limiting BV solutions. In particular, we shall provide a careful description of the jumps and compare the new notion of solutions with the related concepts of energetic and local solutions to rate-independent systems.
Mielke Alexander
Rossi Riccarda
Savar'e Giuseppe
No associations
LandOfFree
BV solutions and viscosity approximations of rate-independent systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with BV solutions and viscosity approximations of rate-independent systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and BV solutions and viscosity approximations of rate-independent systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-720555