Professor Stuart S. Antman
INSTITUTE FOR PHYSICAL SCIENCE AND TECHNOLOGY; INSTITUTE FOR SYSTEMS RESEARCH; UNIVERSITY OF MARYLAND, COLLEGE PARK
A problem for the evolution in time of some system is said to have a quasistatic approximation when the velocity and acceleration are neglected. These derivatives can usually be neglected if they have coefficients that are small parameters. In this case, formal asymptotic methods might exhibit the detailed effects of these parameters. Rigorous asymptotic justifications, which provide error estimates and are typically far harder to carry out, are used by those compulsive about mathematical hygiene, but seldom say more that the formal methods.
The purpose of this lecture is to give rigorous justifications of the quasistatic behavior of solutions of the differential equations governing a couple of conceptually simple problems from particle and continuum mechanics. The justification for these justifications is that the solutions of these simple problems exhibit strange and surprising behavior.