On etudie l'ensemble nul d'une solution u(t,x) de l'equation u t =a(x,t)u xx +b(x,t)u x +C(x,t)u, sous des hypotheses tres generales sur les coefficients a, b, et c

In this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems ( x ′( t ) = f ( x ( t ))), and quasilinear initial value problems ( x ′( t )= A ( x ( t… Expand

This is the first of a two-part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so-called curve shortening of flow-by-mean-curvature… Expand

It is suggested that tension, rather than diffusible molecules generated or sequestered at the leading edge, is the dominant source of long-range inhibition that constrains the spread of the existing front and prevents the formation of secondary fronts.Expand

This work gives an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles and provides a new way to automatically assign texture coordinates to complex undulating surfaces.Expand

This paper presents a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport, and shows how this approach leads to practical algorithms, and demonstrates the method with a number of examples, including those from the medical field.Expand

This work derives a novel gradient descent flow for the computation of the optimal transport map (when it exists) in the Monge-Kantorovich framework, and studies certain properties of the flow, including weak solutions as well as short- and long-term existence.Expand

We give an example of a class of metrics on Sn+1 that evolve under the Ricci Flow into a “neckpinch.” We show that the solution has a Type I singularity, and that the length of the neck, i.e. the… Expand

This work identifies an intrinsic stochastic mechanism through which positive feedback alone is sufficient to account for the spontaneous establishment of a single site of polarity, and finds that the polarization frequency has an inverse dependence on the number of signalling molecules: the frequency of polarization decreases as theNumber of molecules becomes large.Expand