Calculus of Variations and Geometric Measure Theory

F. Riva - G. Scilla - F. Solombrino

Inertial Balanced Viscosity (IBV) solutions to infinite-dimensional rate-independent systems

created by riva on 21 Jun 2023
modified on 22 Jun 2023



Inserted: 21 jun 2023
Last Updated: 22 jun 2023

Year: 2023

ArXiv: 2306.12248 PDF


A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities takes both into account inertial and viscous effects. Under a general set of assumptions it is shown that IBV solutions arise as vanishing inertia and viscosity limits of second order dynamic evolutions as well as of the corresponding time-incremental approximations. Relevant examples coming from applications, such as Allen-Cahn type evolutions and Kelvin-Voigt models in linearized elasticity, are considered.

Keywords: Variational methods, rate-independent systems, vanishing inertia and viscosity limit, minimizing movements scheme, Inertial Balanced Viscosity solutions