Second order approximations of quasistatic evolution problems in finite dimension

In this paper, we study the limit, as epsilon goes to zero, of a particular solution of the equation epsilon(2) A(sic)(epsilon)(t) + epsilon B(u) over dot(epsilon) (t) + del(x)f(t, u(epsilon)(t)) = 0, where f (t, x) is a potential satisfying suitable coerciveness conditions. The limit u (t) of u(epsilon)(t) is piece-wise continuous and verifies del(x)f(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.