Publication: Asymptotic behavior of a weakly forced dry friction oscillator
Full text at PDC
Advisors (or tutors)
Department of Mathematics Texas State University
This note is devoted to stick-slip aspects of the motion of a dry friction damped oscillator under weak irregular forcing. Our main result complements[10, Theorem 3.(a)] and is also related to , where a non-Lipschitz model for Coulomb friction was consider in the unforced case. We provide sufficient conditions guaranteeing that solutions stabilizing in finite time, but observe also an infinite succession of “stick-slip” behavior. The last section discusses an extension to certain systems of such oscillators.
H. Amann and J.I. Díaz; A note on the dynamics of an oscillator in the presence of strong friction, Nonlinear Analysis 55 (2003), 209–216. D. Bothe, Periodic solutions of non-smooth friction oscillators, Z. angew. Math. Phys., 50 (1999), 770–808. H. Brezis; Opérateurs maximaux monotones et semigroupes de contractions, Northholland,Amsterdam, 1972. H. Brezis; Monotone operators, nonlinear semigroups and applications. Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, Canad. Math. Congress, Montreal, Que., 1975, 249–255. A. Cabot, J. I. Díaz, and B. Baji; Asymptotics for some nonlinear damped wave equations: finite time convergence versus exponential decay results, Annales de l’Institut Henri Poincaré C, accepted. J. M. Carlson and J. S. Langer; Properties of earthquakes generated by fault dynamics, Physical Review Letters, 62 (1989), 2632-2635. K. Deimling; Multivalued Differential Equations, Walter de Gruyter, Berlin, New York, 1992. K. Deimling; Resonance and Coulomb friction, Differential Integral Equations 7 (1994), 759–765. K. Deimling and P. Szilágyi; Periodic solutions of dry friction problems, Z. Angew. Math. Phys. 45 (1994), 53–60. K. Deimling, G. Hetzer, and W. Shen; Almost periodicity enforced by Coulomb friction, Adv. Diff. Eq., 1 (1996), 265–281. J. I. Díaz; Special finite time extinction in nonlinear evolution systems: dynamic boundary conditions and Coulomb friction type problems, Proceedings Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann, Zurich, June, 28-30, 2004 (M. Chipot, J. Escher eds.), Birkhäuser, Basel, 2005, 71-97. J. I. Díaz and V. Millot; Coulomb friction and oscillation: stabilization in finite time for a system of damped oscillators, CD-Rom Actas XVIII CEDYA / VIII CMA, Servicio de Publicaciones de la Univ. de Tarragona 2003. K. Kunze, Non-Smooth Dynamical Systems, Lect. Notes Math., vol. 1744, Springer-Verlag, 2000.