I Congreso de Postgrado fcfm: ingeniería, ciencias e innovación

141 Santiago, 10 al 12 de agosto, 2022 13 MOD E L AM I E N TO MAT EMÁT I CO PERTURBED DEGENERATE STATE-DEPENDENT SWEEPING PROCESSES WITH REGULAR AND NONREGULAR SETS Diana Narváez 1 *, Emilio Vilches 2 1 Universidad de Chile, Beauchef 851, Santiago, Chile. 2Universidad de O’Higgins, Av Libertador Bernardo O’Higgins 611, Rancagua, Chile. *Email: dnarvaez@uchile.cl ABSTRACT In this talk, based on [3] and [4], we study the existence of solutions of the so called perturbated degenerate state-dependent sweeping processes. This dynamic was proposed by Kunze and Monteiro-Marques as a model for quasistatic elastoplasticity in [2]. Since then, the degenerate sweeping process has been studied by several authors in the context of convex and prox-regular sets. However, there are not results about perturbated degener- ate state-dependent sweeping processes with nonregular moving sets. We are intended to cover this gap using an appropriate existence result for differential inclusions with single-valued perturbation, and together to a suitable adaptation of the Moreau-Yosida regularization technique by extending the method developed in [1], which allows us to obtain a solution existence result under the assumption that moving sets varies of a Lipschitz way with re- spect to truncated Hausdorff distance. As a consequence we obtain the well-posedness for integrally perturbed degenerate state-dependent sweeping processes. This theoretical results are applied to obtain the well-posed- ness for the online mirror descent method, which is related to the k-server problem. ACKNOWLEDGEMENTS 2 Partially supported by ANID-Chile under grants Fondecyt Regular N° 1220886. REFERENCES [1] A. Jourani and E. Vilches, Regularization of perturbed state-dependent sweeping processes with nonregular sets. J. Nonlinear Convex Anal. 19(4), 633-651 (2018) [2] M. Kunze and M. D. P. Monteiro Marques, Existence of solutions for degenerate sweeping processes. J. Convex Anal. 4 (1), 165-176 (1997) [3] D. Narváez and E. Vilches, Moreau-Yosida Regularization of degenerate state-dependent sweeping processes. J. Optim. Theory Appl. (2022) [4] D. Narváez and E. Vilches, Perturbed degenerate state-dependent sweeping processes with regular and non- regular sets. Submitted (2022)