Parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms

In this work we study a system of parabolic reaction-diffusion equations which are coupled not only through the reaction terms but also by way of nonlocal diffusivity functions. For the associated initial problem, endowed with homogeneous Dirichlet or Neumann boundary conditions, we prove the existence of global solutions. We also prove the existence of local solutions but with less assumptions on the boundedness of the nonlocal terms. The uniqueness result is established next and then we find the conditions under which the existence of strong solutions is assured. We establish several bow-up results for the strong solutions to our problem and we give a criterium for the convergence of these solutions towards a homogeneous state.CAPES [BEX 2478-12-8]; MEC/MCTI/CAPES/CNPq/FAPs, Brazil [71/2013, 88881.030388/2013-01]; Fundacao para a Ciencia e a Tecnologia, Portugal [UID/MAT/04561/2013-2015]info:eu-repo/semantics/publishedVersio

Productivity of Nations: a stochastic frontier approach to TFP decomposition

This paper tackles the problem of aggregate TFP measurement using stochastic frontier analysis (SFA). Data from Penn World Table 6.1 are used to estimate a world production frontier for a sample of 75 countries over a long period (1950-2000) taking advantage of the model offered by Battese & Coelli (1992). We also apply the decomposition of TFP suggested by Bauer (1990) and Kumbhakar (2000) to a smaller sample of 36 countries over the period 1970-2000 in order to evaluate the effects of changes in efficiency (technical and allocative), scale effects and technical change. This allows us to analyze the role of productivity and its components in economic growth of developed and developing nations in addition to the importance of factor accumulation. Although not much explored in the study of economic growth, frontier techniques seem to be of particular interest for that purpose since the separation of efficiency effects and technical change has a direct interpretation in terms of the catch-up debate. The estimated technical efficiency scores reveal the efficiency of nations in the production of non tradable goods since the GDP series used is PPP-adjusted. We also provide a second set of efficiency scores corrected in order to reveal efficiency in the production of tradable goods and rank them. When compared to the rankings of productivity indexes offered by non-frontier studies of Hall & Jones (1996) and Islam (1995) our ranking shows a somewhat more intuitive order of countries. Rankings of the technical change and scale effects components of TFP change are also very intuitive. We also show that productivity is responsible for virtually all the differences of performance between developed and developing countries in terms of rates of growth of income per worker. More important, we find that changes in allocative efficiency play an important role in explaining differences in the productivity of developed and developing nations, even larger than the one played by the technology gap.Total factor productivity, stochastic frontiers, technical change, technical efficiency, allocative efficiency, scale efficiency, convergence

High Performance Hospital Enterprise Architecture

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