Meir (Fiki) Shillor

PUBLISHED ARTICLES

J. Bajkowski, J. Nachman, M. Shillor, and M. Sofonea,
“A model for a Magnetorehological damper,”
Comp. Mathematical Modeling 48 (2008), 56-68.

M'Bagne F. M'Bengue and Meir Shillor;
"Regularity result for the problem of vibrations of a nonlinear beam,"
Electron. J. Diff. Eqns., Vol. 2008(2008), No. 27, pp. 1-12.
The paper

Zhor Lerguet, Meir Shillor, and Mircea Sofonea,
"A frictional contact problem for an electro-viscoelastic body,"
Electron. J. Diff. Eqns., Vol. 2007(2007), No. 170, pp. 1-16.
The paper

K. T. Andrews, S. Anderson, R. S. R. Menike, M. Shillor,
R. Swaminathan, and J. Yuzwalk,
"Vibrations of a damageable string,"
in "Fluids and Waves -- Recent Trends in Applied Analysis,"
F. Botelho, T. Hagen, and J. Jamison (Eds.),
Contemporary Mathematics 440,
AMS, Rhode Island, 2007, pp. 1-14.

Ashraf Zaher, Mohammed Zohdy, Meir Shillor, Abdelnasser Abu-Rezq,
"Stability and control of roll motions of ships," Proceedings of the
Ninth IASTED Intl. Conference on Control and Applications,
May 30 - June 1, 2007, Montreal, Quebec, Canada, pp. 255-260.

M. Campo, J.R. Fernandez, K.L. Kuttler, and M. Shillor,
"Quasistatic evolution of damage in an elastic body: numerical analysis and computatinal
experiments," J. Applied Numerical Mathematics 57(2007), 975-988. Abstract

M. Campo, J.R. Fernandez, K.L. Kuttler, M. Shillor, and J. M. Viano,
"Numerical analysis and simulations of a dynamic frictionless
contact problem with damage," Comput. Meth. Appl. Mech. Engineering,
196 (1-3) (2006), 476--488.      Abstract

K. T. Andrews, L. Guessous, S. Nassar, S. V. Putta, and M. Shillor,
"A one-dimensional spot welding model,"
J. Applied Math. 2006(2006), 1-24,
(Article ID 17936 -- doi:10.1155/JAM/2006/17936). You may download The Article

K.T. Andrews, J. R. Fernandez, and M. Shillor,
“Numerical analysis of dynamic thermoviscoelastic contact with damage of a
rod,” IMA J. Appl. Math. 70(6) (2005), 768 –795.

K.L. Kuttler and M. Shillor,
"Quasistatic Evolution of Damage in an Elastic Body,"
Nonlinear Analysis RWA, 7 (2006), 674-699. Abstract

K.T. Andrews and M. Shillor,
"Thermomechanical behaviour of a damageable
beam in contact with two stops," Applicable Analysis,
85(6-7) (2006), 845-865.   Abstract

K. T. Andrews and M. Shillor,
"Adhesive contact of membranes and beams,"
in "Industrial Mathematics," M.C. Joshi, A.K. Pani, and S.V. Sabnis (Eds.)
Narosa, New Delhi, India, 2006, pp. 13-26.

K. L. Kuttler, M. Shillor and J. R. Fernandez,
"Existence and regularity for dynamic viscoelastic adhesive
contact with damage," Appl. Math. Optim. 53 (2006), 31-66.
Abstract

S. A. Nassar, K. T. Andrews, S. Kruk, and M. Shillor,
"Modelling and simulations of a bonded rod, "
Math. Comput. Modelling, 42 (2005), 553-572.
Abstract

G. Avalos, K.L. Kuttler, and M. Shillor,
"Thermoelastic plate in frictional contact,"
special issue on "Mathematical Inequalities and Applications,"
Bull. Math. Soc. Sc. Math. Roumanie, 48(96)(2) (2005), 103-118.
Abstract

W. A. Lindsey, A. M. Spagnuolo, J. C. Chipman and M. Shillor
"Numerical simulations of a vehicle plarform stabilization,"
Math. Comput. Modelling 41 (2005), 1389-1402. Abstract

José R. Fernández, , Kenneth L. Kuttler, and Meir Shillor,
Analyse numérique d'un problème de contact viscoélastique
sans frottement avec adhérence et endommagement (Numerical
analysis of a viscoelastic frictionless contact problem with
adhesion and damage), Comptes Rendus Mathematique 341(1)
1 July 2005, 63-68 Abstract

M. Sofonea, N. Renon and M. Shillor,
"Stress formulation for frictionless contact of an elastic-perfectly-plastic
body," Applicable Analysis, 83(11)(2004), 1157--1170. Abstract

K. L. Kuttler and M. Shillor,
"Regularity of solutions to a dynamic frictionless contact problem
with normal compliance," Nonlinear Analysis 59 (2004), 1063 - 1075.
Abstract
This is the first major regularity result for contact problems.

K. L. Kuttler and M. Shillor,
"Heat conduction with flux condition on a free patch,"
Appl. Math. Optim. 50(2)(2004), 143-159.
Abstract
An interesting moving boundary problem.

K. T. Andrews, J.R. Fernandez and M. Shillor,
"A Thermoviscoelastic Beam with a Tip Body,"
Computational Mechanics 33(2004), 225-234. Abstract

J. Bajkowski, J. R. Fernandez, M. Shillor and K. L. Kuttler,
"A thermoviscoelastic beam model for brakes," Euro. J. Appl. Math.
15(2)(2004), 181-202,
Abstract
This and the following result deal with a somewhat simplified
model for brakes.

K. L. Kuttler, M. Shillor, and J. R. Fernandez
"Existence for a thermoviscoelastic beam model for brakes,"
Nonlinear Analysis 5(5)(2004), 857-880.
Abstract

K. L. Kuttler and M. Shillor, "Dynamic contact
with Signorini's condition and slip rate dependent friction,"
Electron. J. Diff. Eqns., Vol. 2004(2004), No. 83, pp. 1-21.
Abstract

M. Shillor, M. Sofonea and J. J. Telega,
"Quasistatic viscoelstic contact with friction
and wear diffusion," Quart. Appl. Math. (2) (2004), 379-399.
Abstract

R. J. Gu, M. Shillor, G. Barber and T. Jen,
"Thermal analysis of the grinding process,"
Math. Comput. Modelling 39(9-10) (2004), 991-1003.
Abstract

O. Chau, M. Shillor and M. Sofonea,
"Dynamic frictionless contact with adhesion,"
Z. angew. Math. Phys. (ZAMP) 55(2004), 32-47.
Abstract

B. Oakley, D. Hanna, M. Shillor and G. Barber,
"Ultrasonic parameters as a function of absolute hydrostatic pressure.
II. Mathematical models of the speed of sound in organic liquids,"
J. Phys. Chem. ref. Data 32(4)(2003), 1535 - 1544.
Abstract

K. T. Andrews, L. Chapman, J. R. Fernandez, M. Fisackerly,
M. Shillor, L. Vanerian and T. VanHouten
"A Membrane in Adhesive Contact," SIAM J. Appl. Math.
64(1)(2003), 152 -169.
Abstract

G. C. Barber, M. Jordan-Steen and M. Shillor,
"The heat exchange coefficient in thermoelastic contact,"
J. STLE (3)(2003), 10 - 16.
Abstract

O. Chau, J. R. Fernandez, M. Shillor and M. Sofonea,
"Variational and numerical analysis of a quasistatic viscoelastic
contact problem with adhesion," J. Comput. Appl. Math.
159(2)(2003), 431-465.
Abstract

Y. Dumont, K. L. Kuttler and M. Shillor,
"Analysis and simulations of vibrations of a beam with a slider,"
J. Engineering Mathematics 47 (2003), 61--82.
Abstract

J. R. Fernandez, M. Shillor and M. Sofonea,
"Analysis and numerical simulations of a dynamic contact
problem with adhesion," Math. Comput. Modelling
37(2003), 317 - 1333
Abstract

M. Shillor, M. Sofonea and J. J. Telega,
"Analysis of viscoelstic contact with normal compliance friction
and wear diffusion," C. R. Acad. Sci, Mecanique 331(2003),
395 - 400.
Abstract

K. T. Andrews and M. Shillor,
"Dynamic Adhesive Contact of a Membrane,"
Adv. Math. Sci. Appl. 13(1) (2003), 343 - 356.
Abstract

J. R. Fernandez, M. Shillor and M. Sofonea,
"Numerical analysis of a dynamic viscoelastic contact
problem with adhesion" COMPLAS 2003, VII Intl Conference
on Computational Plasticity.
Abstract

K. T. Andrews and M. Shillor,
"Adhesive contact of membranes and beams,"
Proceedings of the International Conference and Instructional
Workshop in IIT Bombay, 2-9 December 2002.
Abstract,

M. Abdellaoui, A. El Jai and M. Shillor,
"Cellular automata model for a contact problem,"
Math. Comput. Modelling, 36(2002), 1099-1114.
Abstract

H. Gao, G. C. Barber and M. Shillor,
"Numerical simulation of engagement of a wet clutch with
skewed surface roughness," ASME Journal of Tribology
124(2002), 305 - 312.
Abstract

A. Amassad, K. L. Kuttler, M. Rochdi and M. Shillor,
"Quasistatic thermoviscoelastic contact problem
with slip dependent friction coefficient," Math. Comput.
Modelling 36(2002), 839-854.
Abstract

· K. L. Kuttler and M. Shillor,
"Dynamic contact with normal compliance wear and discontinuous
friction coefficient," SIAM J. Math. Anal. 34(1)(2002), 1- 27
Abstract

W. Han, K. L. Kuttler, M. Shillor and M. Sofonea,
"A beam in adhesive contact," in "Contact Mechanics,"
Proceedings of the 3rd Contact Mechanics Intl. Symposium (CMIS),
J.A.C. Martins and M.D.P. Monteiro Marques (Eds.),
Kluwer, Dordrecht, 2002, pp. 277 285.

N. Renon, M. Sofonea and M. Shillor,
"Un mod�le mathŽmatique pour un probl�me de contact
elasto-plastique avec Žcrouissage. Application ˆ la scarification,"
Actes du Dixi\`eme S\'eminaire Franco-Polonais de M\'ecanique},
Institut Polytechnique de Varsovie \& Universit\'e des Sciences et
Technologies de Lille, 2002.
Abstract

K. T. Andrews, K. L. Kuttler, M. Rochdi and M. Shillor,
"One-dimensional thermoviscoelastic contact with damage,"
J. Math. Anal. Appl. 272(2002), 249 - 275.
Abstract

K. T. Andrews and M. Shillor,
"Vibrations of a beam with a damping tip body,"
Math. Comput. Modelling 35(2002), 1033 - 1042.
Abstract

J. R. Fernandez, O. Chau, M. Shillor and M. Sofonea,
"Numerical analysis and simulations of a contact problem
with adhesion," Proceedings of the Fifth World Congress on
Computatuional Mechanics, Vienna, Austria, July 7 - 12, 2002.
Abstract

W. Han, K. L. Kuttler, M. Shillor and M. Sofonea,
"Elastic beam in adhesive contact," Intl. J. Solids
Structures 39(5)(2002), 1145--1164.
Abstract

M. Shillor,
"A survey of 1-D problems of dynamic contact or damage,"
in "From Convexity to Nonconvexity," R. Gilbert,
P. D. Panagiotopoulos and P. Pardalos (Eds.), Kluwer,
Dordrecht, 2001, pp. 283 - 295.

L. Jianu, M. Shillor and M. Sofonea,
"A viscoelastic frictionless contact problem with adhesion,"
Applicable Anal. 80(1-2) (2001), 233--255.
Abstract

A. Amassad, M. Shillor and M. Sofonea,
"A nonlinear evolution inclusion in perfect plasticity with friction,"
Acta Math. Univ. Comenianae LXX(2)(2001), 215 - 228.
Abstract

J. Bajkowski, M. Shillor and P. Tadzik,
"Drgania ukadu belkowego tumionego granulatem: model i identyfikacja
parametrw ukadu," ("Vibrations of beam with granular damping model
and parameter estimation") pp. 97-104, Materiay
VIII Polsko-Francuskiego Seminarium Naukowego Mechaniki
(Proc. of VIII French-Polish Seminary of Mechanics),
Warsaw, Dec. 2001.
Abstract

J. Bajkowski, M. Hac, W. Grzesikiewicz and M. Shillor
"Analysis of frictional properties of braking systems,"
Proc. of the X Sino-Polish Conference on "CAD in Machinery,"
pp 5-12, Warsaw, June 2001.
Abstract

K. L. Kuttler and M. Shillor,
"Vibrations of a beam between two stops,"
Dyn. Continu. Discrete Impuls. Systems 8(1)(2001), 93 - 110.
Abstract

B. Awbi, M. Shillor and M. Sofonea,
"Dual formulation of a quasistatic viscoelastic contact problem
with Tresca friction law," Applic. Anal. 79(2001), 1-20.
Abstract

W. Han, M. Shillor and M. Sofonea,
"Variational and numerical analysis of a quasistatic viscoelastic
problem with normal compliance, friction and damage,"
J. Comp. App. Math. 137(2001), 377-398
Abstract

M Shillor and M. Sofona,
"Variational analysis of quasistatic viscoplastic contact
problems with friction," Comm. Appl. Anal. 5(1)(2001), 135-151
Abstract

K. L. Kuttler, A. Park, M. Shillor and W. Zhang,
"Unilateral dynamic contact of two beams,"
Math. Comput. Modelling 34(2001), 365 - 384.
Abstract

· K. L. Kuttler and M. Shillor,
"Dynamic bilateral contact with discontinuous friction coefficient,"
Nonlinear Anal. 45(2001), 309 - 327.
Abstract

R. Gu and M. Shillor,
"Thermal and wear analysis of an elastic beam in sliding contact,"
Int. J. Solids and Structures 38(14)(2001), 2323-2333.
Abstract

J. R. Fernandez-Garcia, W. Han, M. Shillor and M. Sofonea,
"Numerical analysis and simulations of quasistatic contact problems,"
Intl. J. Appl. Math. Comput. Sci. 11(1)(2001), 205-222.
Abstract

M. Shillor,
"Quasistatic problems in contact mechanics,"
Intl. J. Appl. Math. Comput. Sci. 11(1)(2001), 189-204.
Abstract

D. S. Cameron, N. A. Kheir and M. Shillor,
"Low energy active platform stabilizing suspension system,"
Proceedings of the World Automation Congress - ISIAC,
Maui, Hawaii, June 11-16, 2000.
Abstract

M. Rochdi and M. Shillor,
"Existence and uniqueness for a quasistatic frictional bilateral
contact problem in thermoviscoelasticity,"
Quart. Appl. Math. 58(3)(2000), 543 - 560.

M. Rochdi, M. Shillor and M. Sofonea,
"Analysis of a quasistatic viscoelastic problem with friction
and damage," Adv. Math. Sci. Appl. 10(1)(2000), 173 - 189.

· J. Bajkowski, P. Tadzik, K. T. Andrews and M. Shillor,
"Impulsive response of a beam with granular damping,"
Proceedings of the French-Polish Conference on Materials,
Warsaw University of Technology, Warsaw, November 2000,

M. Shillor, M. Sofonea and R. Touzani,
"Quasistatic frictional contact and wear of a beam,"
Dyn. Continu. Discrete Impuls. Systems (DCDIS)
8(2)(2000), 201 - 218.

M. Cadivel, D. Goeleven and M. Shillor,
"Mathematical study of unilateral oscillators,"
Math. Comput. Modelling 32(3-4)(2000), 381 - 391.

Y. Dumont, D. Goeleven, K. Kuttler, M. Rochdi and M. Shillor,
"A dynamic model of rocks with friction and adhesion, "
J. Math. Anal. Appl. 247(1)(2000), 87-109.
Abstract

C. Chipman, W. Houtz and M. Shillor,
"Simulations of a thermostat-like model I: Approach to steady states,"
Math. Comput. Modelling 32 (2000), 765 - 790.
Abstract

Y. Dumont, D. Goeleven, M. Rochdi and M. Shillor,
"Frictional contact of a nonlinear spring, "
Math. Comput. Modelling 31(2000), 83-97.
Abstract

J. R. F. Garcia, W. Han, M. Shillor and M. Sofonea,
"Recent advances in variational and numerical analysis of
quasistatic contact problems,"
Proceedings of Intl. Symposium MTNS, June 19-23, 2000,
Perpignan, France

M. Shillor and M. Sofonea,
"A quasistatic viscoelastic contact problem with friction,"
Int. J. Engrg. Sci., 38(2000), 1517-1533.

R. Gu, K.L. Kuttler and M. Shillor,
"Frictional wear of a thermoviscoelastic beam,"
J. Math. Anal. Appl., 242(2000) 212-236.

X. Zou, J. Jordan and M. Shillor,
"A dynamic model for a thermostat,"
J. Engn. Math. 36(1999), 291-310.

B. Awbi, M. Shillor and M. Sofonea,
"A contact problem for Bingham fluid with friction,"
Applic. Anal., 72(3-4)(1999), 469-484.

K.L. Kuttler, Y. Renard and M. Shillor,
"Models and simulations of dynamic frictional contact,"
Comp. Meth. Appl. Mech. Engn., 177(1999), 259-272.

B. Cahlon, D. Schmidt, M. Shillorand X. Zou,
"Oscillations in thermostat models,"
Adv. Math. Sci. Appl., 9(1)(1999), 25-49.

K.L. Kuttler and M. Shillor,
"Set-valued pseudomonotone maps and degenerate evolution
inclusions," Comm. Contemp. Math., 1(1)(1999), 87-123.
Our fundamental existence and uniqueness result and its application to the
problem of dynamic frictional contact with slip-rate dependent friction coefficient.

A. Amassad, M. Shillor and M. Sofonea,
"A quasistatic contact problem with slip dependent coefficient of friction,"
Math. Meth. Appl. Sci., 22(1999), 267-248.

The first existence result for the problem of quasistatic frictional contact with
slip-rate, and total slip dependent friction coefficient.

M. Fremond, K. L. Kuttler and M. Shillor,
"Existence and uniqueness of solutions for a one-dimensional damage model,"
JMAA, 229(1999), 271-294.

R. Gariepy, M Shillor and X. Xu,
"Existence of capacity solutions to a model for In Situ Vitrification,"
Euro. J. Appl. Math., 9(6)(1998), 543-559.

M. Rochdi, M. Shillor and M. Sofonea,
"Quasistatic viscoelastic contact with normal compliance and friction,"
J. Elasticity, 51(1998), 105-126 .
The first (existence and) uniqueness result for the problem of quasistatic frictional
contact of a viscoelastic material with normal compliance without any restriction on
the size of the friction coefficient.

A. Amassad, M. Shillor and M. Sofonea,
"A quasistatic contact problem for an elastic perfectly plastic body
with Tresca's friction," Nonlin. Anal. 35(1999), 95-109.

K. T. Andrews, M. Shillor and S. Wright,
"A model for heat transfer in grinding,"
Nonlin. Anal., 35(1999), 233-246.

M. Shillor - Ed.,
"Recent Advances in Contact Mechanics,''
Special Issue of Math. Comput. Modelling 28(4-8)(1998).

A. Mikelic, M. Shillor, and A. Tapiero,
"Homogenization of an elastic material with soft inclusions
within gaps in frictionless contact," Special Issue ``Recent
Advances in Contact Mechanics,'' (M. Shillor-Ed.)
Math. Comput. Modeling 28(4-8)(1998), 287-308.

M. Rochdi, M. Shillor and M. Sofonea,
"A quasistatic contact problem with directional friction and
damped response," Applic. Anal. 68(3-4)(1998) 409-422.

M. Shillor and M. Sofonea,
"A quasistatic contact problem for an elastoplastic rod,"
JMAA, 217(1998) 579-596.

M. Fremond , K. L. Kuttler, B. Nedjar and M. Shillor,
"One-dimensional models of damage,"
Adv. Math. Sci. Appl. 8(2)(1998), 541-570.

K. T. Andrews, A. Klarbring, M. Shillor and S. Wright,
"A dynamic contact problem with friction and wear,"
Int. J. Egng. Sci. 35(14)(1997) 1291-1309.

B. Cahlon, d. Schmidt, M. Shillor and X. Zou,
"Analysis of thermostat models,"
Euro. J. Appl. Math. 8(1997) 437-455.

X. Xu and M. Shillor,
"The Stefan problem with convection and Joule's heating,"
Adv. Diff. Eqns. 2(4)(1997) 667-691.

K. T. Andrews, K. L. Kuttler and M. Shillor,
"On the dynamic behavior of a thermoviscoelastic body in frictional
contact with a rigid obstacle,"
Euro. J. Appl. Math. 8(1997) 417-436.

K. T. Andrews, K. L. Kuttler and M. Shillor,
"Second order evolution equations with dynamic boundary conditions,"
JMAA, 197(1996) 781-795.

K. T. Andrews, M. Shillor and S. Wright,
"On the dynamic vibrations of an elastic beam in frictional contact
with a rigid obstacle," J. Elasticity, 42(1996),1-30.

K. T. Andrews, M. Shillor and S. Wright,
"Dynamic evolution of an elastic beam in frictional contact with an obstacle,"
in "Contact Mechanics", M. Raus, M. Jean, and J.J. Moreau (Eds.),
Plenum, New York, 1995, pp.49-56.

K. L. Kuttler and M. Shillor,
"A dynamic contact problem in one-dimensional thermoviscoelasticity,"
Nonlin. World, 2(1995),355-385.

K. T. Andrews and M. Shillor,
"A Parabolic initial-boundary value problem modeling axially symmetric
thermoelastic contact,"
Nonlin. Anal., 22(12)(1994), 1529-1551.

K. T. Andrews, M. Shillor and S. Wright,
"A hyperbolic-parabolic system modeling the thermoelastic impact of two rods,"
Math. Meth. Appl.Sci. 17(1994), 901-918.

B. Cahlon, I. E. Schochetman and M. Shillor,
"Convective cooling and optimal placement of electronic components with
variable ambient temperature I. The linear model,"
J. Comput. Appl. Math., 47(1993), 357-367.

K. T. Andrews and M. Shillor,
"Asymptotic approximations to one-dimensional problems of quasistatic thermoelastic contact,"
Math. Comput. Modeling, 17(9)(1993), 59-70.

M. Shillor,
"Frictional contact of a beam with an obstacle,"
Proceedings of the Second Int. Conference on Nonlinear Mechanics, W-Z Chien (Ed),
Peking University Press, Beijin, 1993, pp 691-694.

S. D. Howison J. F. Rodrigues and M. Shillor,
"Stationary solutions to the thermistor problem,"
JMAA, 174(2)(1993), 573-588.

P. Shi, M. Shillor and X. Xu,
"Existence of a solution to the Stefan problem with Joule's heating,"
J. Diff. Eqns., 105(2) (1993), 239-263.

K.T. Andrews, P. Shi, M. Shillor and S. Wright,
"Thermoelastic Contact with Barber's heat exchange condition,"
Appl. Math. Opt. 28(1)(1993), 11-48.

C. Cheng and M. Shillor,
"Numerical solutions to the problem of thermoelastic contact of two rods,"
Math. Comput. Modeling, 17(10)(1993), 53-71.

P. Shi and M. Shillor,
"On design of contact patterns in one dimensional thermoelasticity,"
Theoretical Aspects of Industrial Design, V. Komkov and D. A. Fields (Eds),
SIAM, Philadelphia, 1992, pp. 76-82.

A. Klarbring, A. Mikelic and M. Shillor,
"Optimal shape design in contact problems with normal compliance and friction,"
Appl. Math. Letters, 5(2)(1992), 51-55.

P. Shi and M. Shillor,
" Existence of a solution to the n-dimensional problem of thermoelastic contact,"
Comm. Part. Diff. Eq. 17(9 & 10)(1992), 1597-1618.

B. Cahlon, I. E. Schochetman and M. Shillor,
"Optimal placement of heat sources on a rectangular grid,"
J. Math. Compt. Simulation, 34(1992), 351-364.

A. Klarbring, A. Mikelic and M. Shillor,
"The rigid punch problem with friction,"
Int. J. Engng. Sci., 29(1991), 751-768.

P. Shi, M. Shillor and X. L. Zou,
"Numerical solutions to one dimensional problems of thermoelastic contact,"
Comput. Math. Appl., 22(10)(1991), 65-78.

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Meir Shillor shillor@oakland.edu
January 28, 2006