Equivalent formulation and numerical analysis 
of a fire confinement problem

Alberto Bressan; Tao Wang

Displaying similar documents to “Equivalent formulation and numerical analysis of a fire confinement problem”

The geometrical quantity in damped wave equations on a square

Pascal Hébrard, Emmanuel Humbert (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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The energy in a square membrane subject to constant viscous damping on a subset $ω \subset Ω$ decays exponentially in time as soon as satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate $τ (ω)$ of this decay satisfies $τ (ω) = 2 min (- μ (ω), g (ω))$ (see Lebeau [ (1996) 73–109]). Here $μ (ω)$ denotes the spectral abscissa of the damped wave equation operator and $g (ω)$ is a number called the geometrical quantity of and defined as follows. A ray in is the trajectory generated by the free...

Steinhaus chessboard theorem

Władysław Kulpa, Lesƚaw Socha, Marian Turzański (2000)

Acta Universitatis Carolinae. Mathematica et Physica

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Existence of optimal maps in the reflector-type problems

Wilfrid Gangbo, Vladimir Oliker (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we consider probability measures and on a -dimensional sphere in $𝐑^{d + 1}, d \geq 1,$ and cost functions of the form $c (𝐱, 𝐲) = l (\frac{{| 𝐱 - 𝐲 |}^{2}}{2})$ that generalize those arising in geometric optics where $l (t) = - log t .$ We prove that if and vanish on $(d - 1)$ -rectifiable sets, if ${lim}_{t \to 0^{+}} l (t) = + \infty,$ and $g (t) : = t (2 - t) {(l^{'} (t))}^{2}$ is monotone then there exists a unique optimal map that transports onto $ν,$ where optimality is measured against Furthermore, ${inf}_{𝐱} | T_{o} 𝐱 - 𝐱 | > 0 .$ Our approach is based on direct variational arguments. In the special case when $l (t) = - log t,$ existence...