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- Roumen Anguelov, Yves Dumont, Jean M.-S. Lubuma, M. Shillor
- J. Computational Applied Mathematics
- 2014

This work is the numerical analysis and computational companion of the paper by Kamgang and Sallet (Math. Biosc. 213 (2008), pp. 1–12) where threshold conditions for epidemiological models and the global stability of the disease-free equilibrium (DFE) are studied. We establish a discrete counterpart of the main continuous result that guarantees the global… (More)

- J. R. Fernández, Kevin T. Andrews, +4 authors T. VanHouten
- SIAM Journal of Applied Mathematics
- 2003

- ZHOR LERGUET, MEIR SHILLOR, MIRCEA SOFONEA
- 2007

A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a… (More)

- K. T. Andrews, M. F. M’Bengue, M. Shillor, M. SHILLOR
- 2008

This work extends the model developed by Gao (1996) for the vibrations of a nonlinear beam to the case when one of its ends is constrained to move between two reactive or rigid stops. Contact is modeled with the normal compliance condition for the deformable stops, and with the Signorini condition for the rigid stops. The existence of weak solutions to the… (More)

- Ihsan Ömür Bucak, M. A. Zohdy, M. Shillor
- Control and Intelligent Systems
- 2008

Contact phenomena among deformable bodies abound in industry and everyday life, and play an important role in structural and mechanical systems. The complicated surface structure, physics and chemistry involved in contact processes make it necessary to model them with highly complex and nonlinear initial-boundary value problems. Indeed, the now famous… (More)

- M. Shillor, M. Sofonea
- 1999

A problem of frictional contact between an elastic beam and a moving foundation and the resulting wear of the beam is considered. The process is assumed to be quasistatic, the contact is modeled with normal compliance, and the wear is described by the Archard law. Existence and uniqueness of the weak solution for the problem is proved using the theory of… (More)

- M’BAGNE F. M’BENGUE, MEIR SHILLOR
- 2009

Amodel for the dynamics of the Gao nonlinear beam, which allows for buckling, is studied. Existence and uniqueness of the local weak solution was established in Andrews et al. (2008). In this work the further regularity in time of the weak solution is shown using recent results for evolution problems. Moreover, the weak solution is shown to be global,… (More)

- Y. Dumont, D. Goeleven, M. Rochdi, M. Shillor
- 2005

We describe and analyze a frictional problem for a system with a compressed spring which behaves as if it has a spring constant that is negative over a part of its extension range. As a result, the problem has three critical points. The friction is modeled by the Coulomb law. We show that there are three separate stick regions for some values of the… (More)

- M. Shillor
- 2000

form, Problem P . Find fu; ; g such that 0 +K1 +K2 + C1v + S(v; ; ) = Q in V 0; Bv + Au + C2 + 4j(v; ; ; v) 3 f in E 0: Here f 2 E 0 and Q 2 V 0 are given by hf; wi = Z T 0 Z f(t)wi(t) dxdt + Z T 0 Z ij (t)wi;j(t) dxdt + Z T 0 Z N fN(t)wi(t)d dt; hQ; i = Z T 0 hq(t); (t)i dt Z T 0 Z 0(t) (t) dxdt Z T 0 Z C hR( (t) R(t)) (t)d dt Z T 0 Z kij ;i(t) ;j(t) dxdt;… (More)