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Gradient flows with metric and differentiable structures, and applications to the Wasserstein space

Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we summarize some of the main results of a forthcoming book on this topic, where we examine in detail the theory of curves of maximal slope in a general metric setting, following some ideas introduced in [11, 5], and study in detail the case of the Wasserstein space of probability measures. In the first part we derive new general conditions ensuring convergence of the implicit time discretization scheme to a curve of maximal slope, the uniqueness, and the error estimates. In the second...

Green’s function pointwise estimates for the modified Lax–Friedrichs scheme

Pauline Godillon (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to find estimates of the Green’s function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [27] in the continuous viscous setting.

Green's function pointwise estimates for the modified Lax–Friedrichs scheme

Pauline Godillon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to find estimates of the Green's function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [CITE] in the continuous viscous setting.

Harmonic metrics and connections with irregular singularities

Claude Sabbah (1999)

Annales de l'institut Fourier

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L 2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same L 2 complex.

Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics

E. Afenya, S. Mundle (2010)

Mathematical Modelling of Natural Phenomena

Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. The lingering controversies related to various diseases are highlighted. A simple biomathematical model of bone marrow - peripheral blood dynamics in the normal state is proposed and used to investigate cell behavior in normal hematopoiesis from a mathematical viewpoint. Analysis of the steady state and properties of the model are used to make postulations about the...

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