Corporate-NGO Partnerships for Sustainable Development

In the last 15 years, the trend of NGOs working in cooperation with business has developed considerably. The global community – including leaders of international governmental institutions and of the non-profit sector as well as some business leaders – has recognized the importance of including business in the process of international development. NGOs, on the other hand, have become instrumental in development work internationally, but they generally do not have the means and resources to carry out their projects efficiently in a sustainable manner. This is why engaging business with the public and non-profit sectors to find common solutions to problems has been an increasing trend globally. The first section of this paper analyzes the general trend of increasing interaction between the public and the private sector. It outlines some of the benefits of partnerships to both corporations and NGOs, the practical difficulties they present, and the elements necessary to establishing a healthy collaboration between both actors. The second section illustrates the potential of such partnerships by looking at their effectiveness in the fair or ethical trade movement. Partnerships in fair trade seek to address both the economic and social/environmental aspects of sustainable development, so they present benefits and challenges simultaneously. We shall use a case study from the coffee industry, to analyze how a large corporation such as Starbucks works successfully with NGOs to promote sustainable and fair coffee production practices. Finally, we shall discuss the success of partnerships, drawing conclusions from the analysis of the case study

On a model of phase relaxation for the hyperbolic Stefan problem

In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo-Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds

The "strange term" in the periodic homogenization for multivalued Leray-Lions operators in perforated domains

International audienceUsing the periodic unfolding method of Cioranescu, Damlamian and Griso, we study the homogenization for equations of the form -\Div d_\varepsilon=f,\text{ with }\bigl(\nabla u_{\varepsilon , \delta }(x),d_{\varepsilon , \delta }(x)\bigr) \in A_\varepsilon(x) in a perforated domain with holes of size $\varepsilon \delta$ periodically distributed in the domain, where $A_\varepsilon$ is a function whose values are maximal monotone graphs (on $\R^{N})$. Two different unfolding operators are involved in such a geometric situation. Under appropriate growth and coercivity assumptions, if the corresponding two sequences of unfolded maximal monotone graphs converge in the graph sense to the maximal monotone graphs $A(x,y)$ and $A_0(x,z)$ for almost every $(x,y,z)\in \Omega \times Y \times \R^N$, as $\varepsilon \to 0$, then every cluster point $(u_0,d_0)$ of the sequence $(u_{\varepsilon , \delta }, d_{\varepsilon , \delta } )$ for the weak topology in the naturally associated Sobolev space is a solution of the homogenized problem which is expressed in terms of $u_0$ alone. This result applies to the case where $A_{\varepsilon}(x)$ is of the form $B(x/\varepsilon)$ where $B(y)$ is periodic and continuous at $y=0$, and, in particular, to the oscillating $p$-Laplacian

The Periodic Unfolding Method in Homogenization

International audienceThe periodic unfolding method was introduced in 2002 in [Cioranescu, Damlamian, and Griso, C. R. Acad. Sci. Paris, Ser. 1, 335 (2002), pp. 99-104] (with the basic proofs in [Proceedings of the Narvik Conference 2004, GAKUTO Internat. Ser. Math. Sci. Appl. 24, Gakkotosho, Tokyo, 2006, pp. 119-136]). In the present paper we go into all the details of the method and include complete proofs, as well as several new extensions and developments. This approach is based on two distinct ideas, each leading to a new ingredient. The first idea is the change of scale, which is embodied in the unfolding operator. At the expense of doubling the dimension, this allows one to use standard weak or strong convergence theorems in L(p) spaces instead of more complicated tools (such as two-scale convergence, which is shown to be merely the weak convergence of the unfolding; cf. Remark 2.15). The second idea is the separation of scales, which is implemented as a macro-micro decomposition of functions and is especially suited for the weakly convergent sequences of Sobolev spaces. In the framework of this method, the proofs of most periodic homogenization results are elementary. The unfolding is particularly well-suited for multiscale problems (a simple backward iteration argument suffices) and for precise corrector results without extra regularity on the data. A list of the papers where these ideas appeared, at least in some preliminary form, is given with a discussion of their content. We also give a list of papers published since the publication [Cioranescu, Damlamian, and Griso, C. R. Acad. Sci. Paris, Ser. 1, 335 (2002), pp. 99-104], and where the unfolding method has been successfully applied

The periodic unfolding method for perforated domains and Neumann sieve models

AbstractThe periodic unfolding method, introduced in [D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104], was developed to study the limit behavior of periodic problems depending on a small parameter ε. The same philosophy applies to a range of periodic problems with small parameters and with a specific period (as well as to almost any combinations thereof). One example is the so-called Neumann sieve.In this work, we present these extensions and show how they apply to known results and allow for generalizations (some in dimension N⩾3 only). The case of the Neumann sieve is treated in details. This approach is significantly simpler than the original ones, both in spirit and in practice

The periodic unfolding method in domains with holes

We give a comprehensive presentation of the periodic unfolding method for perforated domains, both when the unit hole is a compact subset of the open unit cell and when this is impossible to achieve. In order to apply the method to boundary-value problems with non homogeneous Neumann conditions on the boundaries of the holes, the properties of the boundary unfolding operator are also extensively studied. The paper concludes with applications to such problems and examples of reiterated unfolding

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems

An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all of these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved

A stability result for nonlinear Neumann problems under boundary variations

In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.Comment: 26 page

Homogenization in a thin domain with an oscillatory boundary

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type $R^\epsilon = \{(x,y) \in \R^2; x \in (0,1), 0 < y < \epsilon G(x, x/\epsilon)\}$ where the function G(x,y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter $\epsilon$.Comment: 27 pages, 2 figure