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385
Eikonal equations on the Sierpinski gasket
, 2014
"... We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this lim ..."
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We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize
Wavefronts and solutions of the eikonal equation
"... In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat’s principle, first-order changes in the traveltime can b ..."
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Cited by 1 (0 self)
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In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat’s principle, first-order changes in the traveltime can
Stripe Patterns and the Eikonal Equation
"... In this note we describe the behaviour of a stripe-forming system that arises in the modelling of block copolymers. Part of the analysis concerns a new formulation of the eikonal equation in terms of projections. For precise statements of the results, complete proofs, and references, we refer to [4] ..."
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In this note we describe the behaviour of a stripe-forming system that arises in the modelling of block copolymers. Part of the analysis concerns a new formulation of the eikonal equation in terms of projections. For precise statements of the results, complete proofs, and references, we refer to [4
The Focusing Problem for the Eikonal Equation
"... We study the focusing problem for the eikonal equation t u = i.e., the initial value problem in which the support of the initial datum is outside some compact set in R . The hole in the support will be filled in finite time and we are interested in the asymptotics of the hole as it close ..."
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Cited by 2 (0 self)
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We study the focusing problem for the eikonal equation t u = i.e., the initial value problem in which the support of the initial datum is outside some compact set in R . The hole in the support will be filled in finite time and we are interested in the asymptotics of the hole
Eikonal equations in metric spaces
"... A new notion of a viscosity solution for Eikonal equations in a general metric space is introduced. A comparison principle is established. The existence of a unique solution is shown by constructing a value function of the corresponding optimal control theory. The theory applies to in-nite dimension ..."
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A new notion of a viscosity solution for Eikonal equations in a general metric space is introduced. A comparison principle is established. The existence of a unique solution is shown by constructing a value function of the corresponding optimal control theory. The theory applies to in
A kinetic eikonal equation
- C. R. Math. Acad. Sci. Paris
"... We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t,x) → (t/ε,x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small dif ..."
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Cited by 7 (3 self)
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We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t,x) → (t/ε,x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small
A FAST SWEEPING METHOD FOR EIKONAL EQUATIONS
, 2004
"... In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve the discr ..."
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Cited by 181 (7 self)
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In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve
Integral formulations of the geometric eikonal equation
- Interfaces Free Bound
"... Abstract We prove integral formulations of the eikonal equation ut = c(x, t)|Du|, equivalent to the notion of viscosity solution in the framework of the set-theoretic approach to front propagation problems. We apply these integral formulations to investigate the regularity of the front: we prove th ..."
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Cited by 2 (1 self)
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Abstract We prove integral formulations of the eikonal equation ut = c(x, t)|Du|, equivalent to the notion of viscosity solution in the framework of the set-theoretic approach to front propagation problems. We apply these integral formulations to investigate the regularity of the front: we prove
Adaptation of Eikonal Equation over Weighted
"... Abstract. In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure. This novel approach is based on a family of discrete morphological local and nonlocal gradients expressed by partial difference equations (PdEs). Our formul ..."
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Abstract. In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure. This novel approach is based on a family of discrete morphological local and nonlocal gradients expressed by partial difference equations (PdEs). Our
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