Second order approximations of quasistatic evolution problems in finite dimension

In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation ε 2Aü ε(t) + εBu ε(t) + xf(t; u ε(t)) = 0, where f(t; x) is a potential satisfying suitable coerciveness conditions. The limit u(t) of u ε(t) is piece-wise continuous and veries rxf(t; u(t)) = 0. Moreover, certain jump conditions characterize the behaviour of u(t) at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.