Stuart S. Antman
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Stuart S. Antman
Distinguished University Professor, Joint/Mathematics
Continuum Physics and Nonlinear Analysis
Professor Antman studies a variety of dynamical and steady-state nonlinear problems for rods, shells, and three-dimensional solid bodies. The bodies are composed of nonlinearly elastic, viscoelastic, plastic, viscoplastic, or magnetoelastic materials. In each case, properly invariant, geometrically exact theories encompassing general nonlinear constitutive equations are used. In some cases, the solids interact with fluids. The goals of these studies are to discover new nonlinear effects, determine thresholds in constitutive equations separating qualitatively different responses, treat control problems involving "smart" materials, examine important kinds of instabilities, contribute to the theory of shocks and dissipative mechanisms in solids, and develop new methods of nonlinear analysis and of effective computation for problems of solid mechanics.
Selected publications:
- (with H. Koch) Stability and Hopf bifurcation
for fully nonlinear parabolic-hyperbolic equations, SIAM J. Mathematical Analysis, 32 (2001)
360-384.
- (with L. S. Srubshchik) Asymptotic analysis of
the eversion of nonlinearly elastic shells, II.
Incompressible shells. J. Elasticity, 63 (2001) 171-219.
- (with S.-C. Yip & M. Wiegner) The Motion of a particle on a light viscoelastic bar:
Asymptotic analysis of the
quasilinear parabolic-hyperbolic equation, J.
de Mathe'matiques Pures et Applique'es, 81 (2002), 283-309.
- (with T. I. Seidman) Parabolic-hyperbolic systems
governing the spatial motion
of nonlinearly viscoelastic rods, Arch. Rational Mech. Anal. (2005), 69 pp.
- Nonlinear Problems of Elasticity, 2nd edn., Springer, 2004.
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