@article {1078-0947_2012_4_1125,
	title = {Second order approximations of quasistatic evolution problems in finite dimension},
	journal = {Discrete \& Continuous Dynamical Systems - A},
	volume = {32},
	number = {1078-0947_2012_4_112},
	year = {2012},
	pages = {1125},
	abstract = {<p>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.</p>},
	keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity},
	issn = {1078-0947},
	doi = {10.3934/dcds.2012.32.1125},
	url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8},
	author = {Virginia Agostiniani}
}
