Semilinear Parabolic Problems Define Semiflows on C k Spaces

Mora, Xavier

doi:10.2307/1999300

Cited by 66 publications

(105 citation statements)

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“…where (2) and it satisfies both the maximality and the compactness property (see Mora, 1983). Moreover, it is also possible to prove that the solutions k(x, t) and p(x, t) satisfy:…”

Section: The Solow-type Modelmentioning

confidence: 99%

Pollution diffusion and abatement activities across space and over time

Torre

Liuzzi

Marsiglio

2015

Mathematical Social Sciences

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We analyze the spatio-temporal dynamics of capital and pollution in an economic growth model with purposive environmental protection activities. The production process of a unique homogeneous good generates pollution, thus the increases in output associated with economic growth tend to rise the stock of pollution. Pollution is a negative production externality which thus feeds back on the economy lowering the level of output; in order to compensate for such a negative effect associated with economic development, pollution is reduced by publicly funded abatement activities. We firstly consider a Solow-type framework in which economic and environmental policies are completely exogenous, and then we move to a Ramsey-type context in which they are endogenously determined. We analyze the spatio-temporal dynamics of the model economy through numerical simulations, and we consider two different specifications of the production function (a globally concave and a convex-concave technology) in order to stress the role that eventual poverty traps might play on both economic and environmental outcomes. We show that in the convexconcave technology framework, whenever rich regions are substantially rich diffusion can help poor regions to escape their poverty traps; if however they are not rich enough diffusion might condemn also rich regions to collapse. However, even if rich regions are particularly rich whenever the pollution externality is strong, the whole spatial economy might be doomed to collapse. Forthcoming in Mathematical Social Sciences AbstractWe analyze the spatio-temporal dynamics of capital and pollution in an economic growth model with purposive environmental protection activities. The production process of a unique homogeneous good generates pollution, thus the increases in output associated with economic growth tend to rise the stock of pollution. Pollution is a negative production externality which thus feeds back on the economy lowering the level of output; in order to compensate for such a negative effect associated with economic development, pollution is reduced by publicly funded abatement activities. We firstly consider a Solow-type framework in which economic and environmental policies are completely exogenous, and then we move to a Ramseytype context in which they are endogenously determined. We analyze the spatio-temporal dynamics of the model economy through numerical simulations, and we consider two different specifications of the production function (a globally concave and a convex-concave technology) in order to stress the role that eventual poverty traps might play on both economic and environmental outcomes. We show that in the convex-concave technology framework, whenever rich regions are substantially rich diffusion can help poor regions to escape their poverty traps; if however they are not rich enough diffusion might condemn also rich regions to collapse. However, even if rich regions are particularly rich whenever the pollution externality is strong, the whole spatial economy mi...

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“…where (2) and it satisfies both the maximality and the compactness property (see Mora, 1983). Moreover, it is also possible to prove that the solutions k(x, t) and p(x, t) satisfy:…”

Section: The Solow-type Modelmentioning

confidence: 99%

Pollution diffusion and abatement activities across space and over time

Torre

Liuzzi

Marsiglio

2015

Mathematical Social Sciences

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“…Finally, note that −∆ with boundary conditions given by B is a sectorial operator L 2 (Ω), [3], and from the results in [7] or [1], it is also sectorial in X. Also note that the spectrum of this operator is the same in both spaces.…”

Section: The Rescaled Equationmentioning

confidence: 88%

Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations

Langa¹,

Robinson²,

Rodriguez-Bernal³

et al. 2007

DCDS-A

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“…The finiteness of E and the fact that (1) generates a strongly monotone, completely continuous semiflow on the positive cone in C 1 (Ω) (see [22]) and that…”

Section: Proofsmentioning

confidence: 99%

Asymptotically stable equilibria for monotone semiflows

Hirsch

Smith

2006

Discrete &Amp; Continuous Dynamical Systems - A

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Abstract. Conditions for the existence of a stable equilibrium and for the existence of an asymptotically stable equilibrium for a strongly order preserving semiflow are presented. Analyticity of the semiflow and the compactness of certain subsets of the set of equilibria are required for the latter and yield finiteness of the equilibrium set. Our results are applied to semilinear parabolic partial differential equations and to the classical Kolmogorov competition system with diffusion.

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Semilinear Parabolic Problems Define Semiflows on C k Spaces

Cited by 66 publications

References 0 publications

Pollution diffusion and abatement activities across space and over time

Pollution diffusion and abatement activities across space and over time

Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations

Asymptotically stable equilibria for monotone semiflows

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