Differential, energetic, and metric formulations for rate-independent processes
- Mielke, Alexander
2010 Mathematics Subject Classification
- 49Q20 58E99
- Energetic solutions, BV solutions, parametrized solutions, metric evolutionary systems, metric velocity, metric slope, vanishing-viscosity limit, vanishing-viscosity contact potential, doubly nonlinear equations, Gamma convergence
We consider different solution concepts for rate-independent systems. This includes energetic solutions in the topological setting and differentiable, local, parametrized and BV solutions in the Banach-space setting. The latter two solution concepts rely on the method of vanishing viscosity, in which solutions of the rate-independent system are defined as limits of solutions of systems with small viscosity. Finally, we also show how the theory of metric evolutionary systems can be used to define parametrized and BV solutions in metric spaces.
- A. Mielke, Chapter: Differential, Energetic, and Metric Formulations for Rate-Independent Processes, in: Nonlinear PDE's and Applications, C.I.M.E. Summer School, Cetraro, Italy 2008, L. Ambrosio, G. Savaré, eds., vol. 2028 of Lecture Notes in Mathematics, Springer, Berlin Heidelberg, 2011, pp. 87--167