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Non-trapping sets and Huygens principle

Dario Benedetto; Emanuele Caglioti; Roberto Libero — 1999

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Non-Trapping sets and Huygens Principle

Dario Benedetto; Emanuele Caglioti; Roberto Libero — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the evolution of a set $Λ \subset ℝ^{2}$ according to the Huygens principle: the domain at time , Λ, is the set of the points whose distance from is lower than . We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of , and we give an algorithm to approximate the evolution. Finally we restrict our attention...

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