Search results for " math"

A note on Jordan’s inequality

2020

Abstract In this paper we obtain some bounds in terms of polynomials for the function sin x x {{\sin x} \over x} , x ∈ [0, π].

Optimal mass transportation for costs given by Finsler distances via p-Laplacian approximations

2016

Abstract In this paper we approximate a Kantorovich potential and a transport density for the mass transport problem of two measures (with the transport cost given by a Finsler distance), by taking limits, as p goes to infinity, to a family of variational problems of p-Laplacian type. We characterize the Euler–Lagrange equation associated to the variational Kantorovich problem. We also obtain different characterizations of the Kantorovich potentials and a Benamou–Brenier formula for the transport problem.

ORBITALLY NONEXPANSIVE MAPPINGS

2015

We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient ter…

2011

Abstract In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum: where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator, sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.

Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research

2004

International audience; .This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by n…

Global solutions of aerotaxis equations

2017

We study the existence of the global solutions in a model de- scribing the evolution of density of bacteria and oxygen dissolved in water lling a capillary. In the proof of local existence of classical solutions we use Amann theory. The Moser{Alikakos technique is the main tool for the proof of L1 boundedness of local solutions.

On Whitham and Related Equations

2017

The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular, we establish rigorous bounds between solutions of the Whitham and Korteweg–de Vries equations and provide some insights into the dynamics of the Whitham equation in different regimes, some of them being outside the range of validity of the Whitham equation as a water waves model.

Linear Approximation Property, Minkowski Dimension, and Quasiconformal Spheres

1990

Complex Analysis and Dynamical Systems VII

2017

L∞-variational problems associated to measurable Finsler structures

2016

Abstract We study L ∞ -variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.