01260nas a2200193 4500008004100000022001400041245008600055210006900141300000900210490000700219520060600226653002800832653002500860653002800885653002700913653002400940100002600964856007600990 2012 eng d a1078-094700aSecond order approximations of quasistatic evolution problems in finite dimension0 aSecond order approximations of quasistatic evolution problems in a11250 v323 a
In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. 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.
10adiscrete approximations10aperturbation methods10asaddle-node bifurcation10aSingular perturbations10avanishing viscosity1 aAgostiniani, Virginia uhttp://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8