# Non-Trapping sets and Huygens Principle

Dario Benedetto; Emanuele Caglioti; Roberto Libero

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 3, page 517-530
- ISSN: 0764-583X

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topBenedetto, Dario, Caglioti, Emanuele, and Libero, Roberto. "Non-Trapping sets and Huygens Principle." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 517-530. <http://eudml.org/doc/197469>.

@article{Benedetto2010,

abstract = {
We consider the evolution of a set $\Lambda\subset \mathbb R^2$ according to the
Huygens principle: i.e. the domain at time t>0, Λt,
is the set of
the points whose distance from Λ is lower than
t. 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 t, and
we give an algorithm to approximate the evolution.
Finally we restrict our attention to the class of sets for which the
turning angle of the boundary is greater than -π (see [2]).
For this class of sets we prove that the perimeter is a
Lipschitz-continuous function of t.
This evolution problem is relevant for the applications
because it is used as a model for solid fuel combustion.
},

author = {Benedetto, Dario, Caglioti, Emanuele, Libero, Roberto},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Eikonal equation; distance function.; eikonal equation; distance function; solid fuel combustion},

language = {eng},

month = {3},

number = {3},

pages = {517-530},

publisher = {EDP Sciences},

title = {Non-Trapping sets and Huygens Principle},

url = {http://eudml.org/doc/197469},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Benedetto, Dario

AU - Caglioti, Emanuele

AU - Libero, Roberto

TI - Non-Trapping sets and Huygens Principle

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 3

SP - 517

EP - 530

AB -
We consider the evolution of a set $\Lambda\subset \mathbb R^2$ according to the
Huygens principle: i.e. the domain at time t>0, Λt,
is the set of
the points whose distance from Λ is lower than
t. 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 t, and
we give an algorithm to approximate the evolution.
Finally we restrict our attention to the class of sets for which the
turning angle of the boundary is greater than -π (see [2]).
For this class of sets we prove that the perimeter is a
Lipschitz-continuous function of t.
This evolution problem is relevant for the applications
because it is used as a model for solid fuel combustion.

LA - eng

KW - Eikonal equation; distance function.; eikonal equation; distance function; solid fuel combustion

UR - http://eudml.org/doc/197469

ER -

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