Existence of solutions for a Lipschitzian vibroimpact problem with time-dependent constraints
Tóm tắt
Từ khóa
Tài liệu tham khảo
Adly, S., Haddad, T.: Well-posedness of nonconvex degenerate sweeping process via unconstrained evolution problems. Nonlinear Anal. Hybrid Syst. 36, 100832 (2020)
Adly, S., Nacry, F., Thibault, L.: Preservation of prox-regularity of sets with applications to constrained optimization. SIAM J. Optim. 26, 448–473 (2016)
Attouch, H., Cabot, A., Redont, P.: The dynamics of elastic shocks via epigraphical regularization of a differential inclusion. Barrier and penalty approximations. Adv. Math. Sci. Appl. 12(1), 273–306 (2002)
Attouch, H., Maingé, P.E., Redont, P.: A second-order differential system with Hessian-driven damping; application to non-elastic shock laws. Differ. Equ. Appl. 4(1), 27–65 (2012)
Aubin, J.-P., Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory. Springer, Berlin (1984)
Ballard, P.: The dynamics of discrete mechanical systems with perfect unilateral constraints. Arch. Ration. Mech. Anal. 154, 199–274 (2000)
Bernicot, F., Lefebvre-Lepot, A.: Existence results for nonsmooth second-order differential inclusions, convergence result for a numerical scheme and application to the modeling of inelastic collisions. Confluentes Math. 2, 445–471 (2010)
Bernicot, F., Venel, J.: Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme. J. Differ. Equ. 251, 1195–1224 (2011)
Bernicot, F., Venel, J.: Existence of solutions for second-order differential inclusions involving proximal normal cones. J. Math. Pures Appl. 9(98), 257–294 (2012)
Bounkhel, M.: Existence results for first and second order nonconvex sweeping processes with perturbations and with delay: fixed point approach. Georgian Math. J. 13, 239–249 (2006)
Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2010)
Cabot, A., Paoli, L.: Asymptotics for some vibroimpact problems with a linear dissipation term. J. Math. Pures Appl. (9) 87(3), 291–323 (2007)
Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
Colombo, G., Thibault, L.: Prox-regular sets and applications. In: Handbook of Nonconvex Analysis and Applications, Somerville, pp. 99–182 (2010)
Dzonou, R., Monteiro Marques, M.D.P.: A sweeping process approach to inelastic contact problems with general inertia operators. Eur. J. Mech. A, Solids 26, 474–490 (2007)
Dzonou, R., Monteiro Marques, M.D.P., Paoli, L.: A convergence result for a vibro-impact problem with a general inertia operator. Nonlinear Dyn. 58, 361–384 (2009)
Hartman, P.: Ordinary Differential Equations. Wiley, New York (1964)
Mabrouk, M.: A unified variational model for the dynamics of perfect unilateral constraints. Eur. J. Mech. A, Solids 17, 819–842 (1998)
Maury, B.: A time-stepping scheme for inelastic collisions. Numerical handling of the nonoverlapping constraint. Numer. Math. 102, 649–679 (2006)
Monteiro Marques, M.D.P.: Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction. Birkhäuser, Basel (1993)
Moreau, J.-J.: Liaisons unilatérales sans frottement et chocs inélastiques. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 296, 1473–1476 (1983)
Moreau, J.-J.: Standard inelastic shocks and the dynamics of unilateral constraints. In: Del Piero, G., Maceri, F. (eds.) Unilateral Problems in Structural Analysis, pp. 173–221. Springer, New York (1985)
Moreau, J.-J.: Bounded variation in time. In: Moreau, J.J., Panagiotopoulos, P.D., Strang, G. (eds.) Topics in Nonsmooth Mechanics, pp. 1–74. Birkhäuser, Basel (1988)
Moreau, J.-J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.) Nonsmooth Mechanics and Applications. CISM Courses and Lectures, vol. 302, pp. 1–82. Spinger-Verlag, New York (1988)
Paoli, L.: An existence result for non-smooth vibro-impact problems. J. Differ. Equ. 211, 247–281 (2005)
Paoli, L.: Time-stepping approximation of rigid-body dynamics with perfect unilateral constraints. I: the inelastic impact case. Arch. Ration. Mech. Anal. 198, 457–503 (2010)
Paoli, L.: A position-based time-stepping algorithm for vibro-impact problems with a moving set of constraints. Confluentes Math. 3, 263–290 (2011)
Paoli, L.: A proximal-like algorithm for vibro-impact problems with a non-smooth set of constraints. In: Discrete Contin. Dyn. Syst., Dynamical Systems, Differential Equations and Applications. 8th AIMS Conference. Suppl. Vol. II, pp. 1186–1195 (2011)
Paoli, L.: Existence and approximation for vibro-impact problems with a time-dependent set of constraints. Math. Comput. Simul. 118, 302–309 (2015)
Paoli, L.: Mathematical aspects of vibro-impact problems. In: Advanced Topics in Nonsmooth Dynamics, pp. 135–189. Springer, Cham (2018)
Paoli, L., Schatzman, M.: Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: cas avec perte d’énergie. RAIRO Modél. Math. Anal. Numér. 27, 673–717 (1993)
Paoli, L., Schatzman, M.: Schéma numérique pour un modèle de vibrations avec contraintes unilatérales et perte d’énergie aux impacts, en dimension finie. C. R. Acad. Sci., Sér. 1 Math. 317, 211–215 (1993)
Paoli, L., Schatzman, M.: A numerical scheme for impact problems. I. The one-dimensional case. SIAM J. Numer. Anal. 40, 702–733 (2002)
Paoli, L., Schatzman, M.: A numerical scheme for impact problems. II. The multidimensional case. SIAM J. Numer. Anal. 40, 734–768 (2002)
