2023/06/21 by Filippo Riva, Giovanni Scilla, Riva, Filippo +3
Chemical Engineering · Engineering · #35A15 #49J40 #49S05 #70G75 #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Functional Analysis (math.FA) #Rheology and Fluid Dynamics Studies #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2306.12248
openalex publication_date 2023/06/21 · openalex created_date 2023/06/24 · openalex updated_date 2026/08/01
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.