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Slow motion for gradient systems with equal depth multiple-well potentials
Fabrice Bethuel, Didier Smets, Giandomenico Orlandi
For scalar reaction-diffusion in one space dimension, it is known for a long time that fronts move with an exponentially small speed for potentials with several distinct mini- mize…
On the linear wave regime of the Gross-Pitaevskii equation
Fabrice Bethuel, Raphael Danchin, Didier Smets
We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occ…
Remarks on a Sobolev-Hardy inequality
S. Secchi, D. Smets, M. Willem
We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some op…