Well‐posedness for the FENE dumbbell model of polymeric flows

We prove local and global well‐posedness for the FENE dumbbell model for a very general class of potentials. Indeed, in prior local or global well‐posedness results, conditions on the strength of the singularity (or on the parameter b) were made. Here we give a proof in the general case. We also prove global existence results if the data is small or if we restrict to the co‐rotational model in dimension 2. © 2008 Wiley Periodicals, Inc.     

Generating and Adding Flows on Locally Complete Metric Spaces

As a generalization of a vector field on a manifold, the notion of an arc field on a locally complete metric space was introduced in Bleecker and Calcaterra (J Math Anal Appl, 248: 645–677, 2000). In that paper, the authors proved an analogue of the Cauchy–Lipschitz Theorem, i.e they showed the existence and uniqueness of solution curves for a time independent arc field. In this paper, we extend the result to the time dependent case, namely we show the existence and uniqueness of solution curves for a time dependent arc field. We also introduce the notion of the sum of two time dependent arc fields and show existence and uniqueness of solution curves for this sum.     

Forced convection magnetohydrodynamic Al2O3–Cu/water hybrid nanofluid flow over a backward-facing step

Forced convection hybrid nanofluid flow over a backward-facing step under a non-uniform magnetic field is numerically studied using a finite volume method. The external magnetic source is placed in the step edge. The study is performed for a range of nanoparticles volume fraction, φ, from 0 to 2%, Hartmann number, Ha, from 0 to 50, and Reynolds number, Re, from 100 to 300. Results show that the reattachment length reduces by increasing volume fraction of nanoparticles and by decreasing Reynolds number. The recirculation bubble weakens and the conductive heat transfer mode growth by increasing Hartmann number at weak magnetic field intensity. It totally disappears at high Hartmann number when the convective mode dominates. The average Nusselt number increases by increasing volume fraction of nanoparticles and varies with the Hartmann number. The effects of Lorentz force and hybrid nanoparticles on the heat transfer enhancement rates are strongly linked with volume fraction of nanoparticles and Hartmann and Reynolds numbers.

     

On the Existence of Positive Solutions of Nonlinear Elliptic Equations

We study the existence of positive solutions of the nonlinear elliptic problem in D with u=0 on D, where and are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in ^d(d3). When g is superlinear at 0 and 0f(t)t for t(0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem.     

From compressible to incompressible materials via an asymptotic expansion

Summary. In linear elasticity problems, the pressure is usually introduced for computing the incompressible state. In this paper is presented a technique which is based on a power series expansion of the displacement with respect to the inverse of Lamé's coefficient . It does not require to introduce the pressure as an auxiliary unknown. Moreover, low degree finite elements can be used. The same technique can be applied to Stokes or Navier-Stokes equations, and can be extended to more general parameterized partial differential equations. Discretization error and convergence are analyzed and illustrated by some numerical results. Received April 21, 2000 / Revised version received February 28, 2001 / Published online October 17, 2001     

无界域上1-集弱压缩算子的新不动点结果

本文证明Banach空间中无界域上一类弱序列连续和1-集弱压缩算子的若干新不动点定理.我们引入原点处弱半闭算子,得到该算子的若干不动点定理.进而将著名的Leray-Schauder不动点定理、Altman定理、Roth定理和Petryshyn定理推广到弱序列连续算子和1-集弱压缩算子以及原点处弱半闭算子的情形.本文的主要结果依赖于非紧性弱原子测度的有关条件.     

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.     

The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution

In this paper, we essentially compute the set of x,y>0 such that the mapping \(z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}\) is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ ^*x exists.     

Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population

Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L ₁-setting. Besides, a topological structure of the set of solutions is provided.     

Measures of weak noncompactness and fixed point theory for 1-set weakly contractive operators on unbounded domains

The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive (μ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.