2023/06/15 by Livia Betz, Betz, Livia
Economics, Econometrics and Finance · Engineering · Mathematics · #34G25 #49J40 #49J53 #74P99 #74R99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.09081
openalex publication_date 2023/06/15 · openalex created_date 2023/06/17 · openalex updated_date 2026/07/28
This paper investigates rate-independent systems (RIS), where the dissipation functional depends not only on the rate but also on the history of the state. The latter is expressed in terms of an integral operator. We establish an existence result for the original problem and for the control thereof, without resorting to smallness assumptions. Under a smoothness condition, we prove the uniqueness of solutions to a certain class of history-dependent RIS where the subdifferential of the dissipation potential is an unbounded operator. In this context, we derive an essential estimate that opens the door to future research on the topic of optimization.