Applied And Industrial Mathematics in Italy: Proceedings of by Vanda Valente, Mario Primicerio, Renato Spigler

By Vanda Valente, Mario Primicerio, Renato Spigler

Commercial arithmetic is evolving into a major department of arithmetic. Mathematicians, in Italy specifically, have gotten more and more conscious of this new development and are engaged in bridging the space among hugely really good mathematical examine and the rising call for for innovation from undefined. during this recognize, the contributions during this quantity offer either R&D employees in with a normal view of latest abilities, and lecturers with cutting-edge functions of arithmetic to real-world difficulties, that can even be integrated in complicated classes.

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R<0O such that lim s+m ~ s - 2= 0 ( +- lim Es = 0). s+cc The behaviour of the corresponding solutions ( a s , u s )in the limit s + 00 has been studied in Ref. 1. It turns out that us converge to a Dirac mass concentrated at the origin, whose rescaled profile is a symmetric concave parabola determined by M : The limiting profile is a parabola, but does not give any information on its rate of convergence with respect to rs = ( p s ,eS). The next result concerns the rate of convergence of u s : as710g (d) -+ 9M3 as s -+ 00.

For a review of literature about undesirable economic growth see 5. 2. The model We analyze growth dynamics in an economy where there exists a continuum of identical economic agents. At each instant of time t representative agent’s welfare depends on three goods: leisure 1 - Z(t), where Z(t) is representative agent’s labour input; a free access flow of a renewable environmental good E ( t ) ;a private good which can be consumed as a substitute for the environmental good (cg(t)) or to satisfy different needs (cl(t)).

Using this approximated f , a closed system of conservation laws is obtained which is hyperbolic in the regions of physical interest. In Ref. 31, a suitable scaling has been introduced, t = 0( l / S 2) , x = 0 ( 1 / 6 ) , where TW v = O(S), s = O(S), TW = O(l/S2), (21) is defined from the energy production rate cw = - w - wo and Wo is the equilibrium energy. This scaling yields the following compatibility conditions: + &(nvi) = 0, &(nW)+ &(nSi)+ nqViEi = nCw, atn (23) (24) with the constitutive equations v = Dll(W)Vlog(n) + D 1 2 ( w ) v w f 013(w)v(p, S = D21(W)Vlog(n) + 0 2 2 (W)Vw + 023(W)V(p.

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