143 research outputs found
Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach
We perform a convergence analysis of a discrete-in-time minimization scheme
approximating a finite dimensional singularly perturbed gradient flow. We allow
for different scalings between the viscosity parameter and the
time scale . When the ratio diverges, we
rigorously prove the convergence of this scheme to a (discontinuous) Balanced
Viscosity solution of the quasistatic evolution problem obtained as formal
limit, when , of the gradient flow. We also characterize the
limit evolution corresponding to an asymptotically finite ratio between the
scales, which is of a different kind. In this case, a discrete interfacial
energy is optimized at jump times
Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays
We consider the celebrated Cucker-Smale model in finite dimension, modelling
interacting collective dynamics and their possible evolution to consensus. The
objective of this paper is to study the effect of time delays in the general
model. By a Lyapunov functional approach, we provide convergence results to
consensus for symmetric as well as nonsymmetric communication weights under
some structural conditions
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