Journal•ISSN: 0764-4442
Comptes Rendus De L Academie Des Sciences Serie I-mathematique
Elsevier BV
About: Comptes Rendus De L Academie Des Sciences Serie I-mathematique is an academic journal. The journal publishes majorly in the area(s): Partial differential equation & Boundary value problem. Over the lifetime, 2302 publications have been published receiving 30223 citations.
Topics: Partial differential equation, Boundary value problem, Bounded function, Nonlinear system, Dirichlet problem
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors studied critical site percolation on triangular lattice and introduced harmonic conformal invariants as scaling limits of certain probabilities and calculated their values, and proved the existence, uniqueness, and conformality of the continuum scaling limit.
Abstract: In this Note we study critical site percolation on triangular lattice. We introduce harmonic conformal invariants as scaling limits of certain probabilities and calculate their values. As a corollary we obtain conformal invariance of the crossing probabilities (conjecture attributed to Aizenman by Langlands, Pouliot, and Saint-Aubin in [7]) and find their values (predicted by Cardy in [4], we discuss simpler representation found by Carleson). Then we discuss existence, uniqueness, and conformal invariance of the continuum scaling limit. The detailed proofs appear in [10].
910 citations
TL;DR: In this article, it was shown that the Lorenz equations support a strange attractor, and that the attractor persists under small perturbations of the coefficients in the underlying differential equations.
Abstract: We prove that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coefficients in the underlying differential equations. The proof is based on a combination of normal form theory and rigorous numerical computations.
613 citations
TL;DR: In this article, a schema permettant de profiter d'une architecture parallele for discretisation en temps d'un equation d'evolution aux derivees partielles is proposed.
Abstract: Resume On propose dans cette Note un schema permettant de profiter d'une architecture parallele pour la discretisation en temps d'une equation d'evolution aux derivees partielles. Cette methode, basee sur un schema d'Euler, combine des resolutions grossieres et des resolutions fines et independantes en temps en s'inspirant de ce qui est classique en espace. La parallelisation qui en resulte se fait dans la direction temporelle ce qui est en revanche non classique. Elle a pour principale motivation les problemes en temps reel, d'ou la terminologie proposee de «parareel ».
491 citations
TL;DR: In this paper, a blow-up result for nonlinear wave equations with a damping term was proved, and it was shown that the critical exponent belongs to the blowup case.
Abstract: Using a different and much shorter approach, we prove a blow-up result which is more general than the interesting blow-up result of G Todorova and B Yordanov concerning a nonlinear wave equation with a damping term We also show that the critical exponent belongs to the blow-up case This problem had been left open by these authors
299 citations
TL;DR: In this paper, the convergences to the optimal filter of such approximations of the nonlinear filtering equations were proved, yielding what seemed to be the first mathematically well-founded convergence results for such approximation.
Abstract: In this Note, we study interacting particle approximations of discrete time and measure valued dynamical systems. Such systems have arisen in such diverse scientific disciplines as in Propagation of Chaos Theory (see [12] and [19]), and in Nonlinear Filtering Theory. The main contribution of this Note is to prove the convergences to the optimal filter of such approximations, yielding what seemed to be the first mathematically well-founded convergence results for such approximations of the nonlinear filtering equations. This new treatment was influenced primarily by the development of genetic algorithms (see [16] and [3]), and secondarily by the papers of H. Kunita and L. Stettner, [17] and [18] respectively.
259 citations