Faculty William J. Hrusa, Professor and Associate Department Head
Ph.D., Brown University
E-mail: wh15@andrew.cmu.edu
Office: Wean Hall 7107
Phone: 412-268-8487

Research:

Partial differential equations, integral equations, and calculus of variations are my main areas of research, with particular emphasis on problems that arise in continuum mechanics. Earlier efforts were devoted primarily to the mathematical theory of viscoelasticity, initial-boundary value problems in nonlinear elasticity, thermal effects in elasticity and viscoelasticity, and hyperbolic models for heat conduction. Current research is focused on Lavrentiev’s phenomenon in the calculus variations, i.e. with situations in which the infimum for a given variational problem is sensitive to the precise degree of regularity that is assumed for the competing functions. A major goal is to understand if this phenomenon can occur for realistic problems in nonlinear elasticity.

Selected Publications:

• K. Dani, W.J. Hrusa, & V.J. Mizel, “Lavrentiev’s phenomenon for totally unconstrained variational problems in one dimension”, Nonlinear Diff. Equations Appl. 7, 435-446 (2000).
• B. Doytchinov, W.J. Hrusa, & S. Watson, “On perturbations of differentiable semigroups”, Semigroup Forum 54, 100-111 (1997).
• M.E. Gurtin & W.J. Hrusa, “On the thermodynamics of viscoelastic materials of single-integral type”, Q. Applied Math. 49, 67-85 (1991).
• W.J Hrusa & S. Messaoudi, “On formation of singularities in one-dimensional nonlinear thermoelasticity”, Arch. Rational Mech. Anal. 111, 131-151 (1990).
• M. Renardy, W.J. Hrusa, & J.A. Nohel, Mathematical Problems in Viscoelasticity, Longman, Essex (England), and Wiley, New York, 1987.
• C.M Dafermos & W.J. Hrusa, “Energy Methods for quasilinear hyperbolic initial-boundary value problems: Applications to elastodynamics, Arch. Rational Mech. Anal. 87, 267-292 (1985).