On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group

Franco, José A.

doi:10.3842/sigma.2013.011

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…Progress in the proof of the formula was made by Moretti [11] and Franco [12] for globally hyperbolic spacetimes. However, in their versions the functions appearing in (9) were not differentiable everywhere a fact which was a little annoying since in Connes' program the Dirac operator acts on them.…”

Section: The Distance Formulamentioning

confidence: 99%

“…Similar versions, in which some of the functions F , F do not exist hold true. One has just to drop the corresponding inequalities in (12).…”

Section: The Distance Formulamentioning

confidence: 99%

“…The proof uses Theorem 2.2, a previous construction of steep functions by the author [17], stability results for Cauchy temporal functions and Lorentzian distance [1], and a previous nondifferentiable version of the distance formula proved by Franco [12] (thus it is certainly not self contained). For shortness the final step in the proof assumes familiarity with Franco's paper and more generally with the details of [12,17]. A Cauchy time function is a time function whose restriction to any inextendible continuous causal curve has image R. In the next theorems F is as in Eq.…”

Section: A Second Proofmentioning

confidence: 99%

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The representation of spacetime through steep time functions

Minguzzi

2017

Preprint

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In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid for globally hyperbolic Lorentzian spacetimes.

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Section: The Distance Formulamentioning

confidence: 99%

“…Similar versions, in which some of the functions F , F do not exist hold true. One has just to drop the corresponding inequalities in (12).…”

Section: The Distance Formulamentioning

confidence: 99%

Section: A Second Proofmentioning

confidence: 99%

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The representation of spacetime through steep time functions

Minguzzi

2017

Preprint

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“…The set C is called the causal cone and its elements are smooth bounded causal functions. In a globally hyperbolic spacetime (M, g), the geodesic distance coincides with the Lorentzian distance function [10] d…”

Section: Lorentzian Spectral Triplementioning

confidence: 99%

Noncommutative geometrical origin of the energy-momentum dispersion relation

Watcharangkool

Sakellariadou

2017

Phys. Rev. D

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We investigate a link between the energy-momentum dispersion relation and the spectral distance in the context of a Lorentzian almost-commutative spectral geometry, defined by the product of Minkowski spacetime and an internal discrete noncommutative space. Using the causal structure, the almost-commutative manifold can be identified with a pair of four-dimensional Minkowski spacetimes embedded in a five-dimensional Minkowski geometry. Considering fermions travelling within the light cone of the ambient five-dimensional spacetime, we then derive the energy-momentum dispersion relation. a email address: apimook.watcharangkool@kcl.ac.uk

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“…However, these constructions can be used in some nonlinear equations as well. Some examples can be found in [6,11,12].…”

Section: Introductionmentioning

confidence: 99%

Global Actions of the Lie Symmetries of the Nonlinear Filtration Equation

Franco¹

2014

Preprint

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The classification of the Lie point symmetries of the nonlinear filtration equation gives the generic case and three special cases. By restricting to a special class of functions, we show that the Lie symmetries of the nonlinear filtration equation exponentiate to a global action of a solvable Lie group in the generic case and two of the three special cases. We show that the action of the Lie point symmetries cannot be globalized for the third special case.

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On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group

Abstract: Abstract. By restricting to a special class of smooth functions, the local action of the symmetry group is globalized. This special class of functions is constructed using parabolic induction.

Cited by 4 publications

References 16 publications

The representation of spacetime through steep time functions

The representation of spacetime through steep time functions

Noncommutative geometrical origin of the energy-momentum dispersion relation

Global Actions of the Lie Symmetries of the Nonlinear Filtration Equation

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