Inserted: 18 mar 2010
Last Updated: 26 mar 2011
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
We study of the Chapman-Rubinstein-Schatzman evolution model for superconductivity, viewed as a gradient flow on the space of measures equipped with the quadratic Wasserstein structure. We consider general signed measures, as in the physical model. Understanding the evolution as a gradient flow in this context gives rise to several new questions, in particular how to define a ``Wasserstein" distance for signed measures. We generalize the minimizing movement scheme in this context, we show that the one step regularity estimates hold as in the positive case, and derive an evolution equation for the measure which contains an error term compared to the Chapman-Rubinstein-Schatzman model. Moreover, we also show the same applies to a very similar dissipative model on the whole plane.