Search Results - "LeFloch, Philippe G."

Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces by Le Floch, Bruno, LeFloch, Philippe G., Veneziano, Gabriele

“…A bstract For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity…”
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Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study by Yangyang Cao, Yangyang Cao, Mohammad A. Ghazizadeh, Mohammad A. Ghazizadeh, Philippe G. LeFloch, Philippe G. LeFloch

“…We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or…”
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A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes by Beyer, Florian, LeFloch, Philippe G.

“…We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method…”
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The Euclidean-hyperboloidal foliation method: application to f(R) modified gravity by LeFloch, Philippe G., Ma, Yue

“…This paper is a part of a series devoted to the Euclidean-hyperboloidal foliation method introduced by the authors for investigating the global existence…”
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Late-time asymptotic behavior of solutions to hyperbolic conservation laws on the sphere by Beljadid, Abdelaziz, LeFloch, Philippe G., Mohammadian, Abdolmajid

“…We consider nonlinear hyperbolic conservation laws posed on a curved geometry, referred to as “geometric Burgers equations” after Ben-Artzi and LeFloch (2007),…”
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The mathematical theory of splitting-merging patterns in phase transition dynamics by Kardhashi, Eva, Laforest, Marc, LeFloch, Philippe G.

“…For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear…”
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A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime by LeFloch, Philippe G., Thanh, Mai Duc

“…► We investigate the Riemann problem for the shallow water equations with discontinuous topography. ► We investigate the existence and uniqueness of Riemann…”
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Self-gravitating fluid flows with Gowdy symmetry near cosmological singularities by Beyer, Florian, LeFloch, Philippe G.

“…We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus T 3 and, in this class, we solve the singular initial value…”
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Kinetic Functions for Nonclassical Shocks, Entropy Stability, and Discrete Summation by Parts by LeFloch, Philippe G., Ranocha, Hendrik

“…We study nonlinear hyperbolic conservation laws with non-convex flux in one space dimension and, for a broad class of numerical methods based on summation by…”
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Mesh-free error integration in arbitrary dimensions: A numerical study of discrepancy functions by LeFloch, Philippe G., Mercier, Jean-Marc

“…We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their…”
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Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds by Dong, Shijie, LeFloch, Philippe G., Wyatt, Zoe

“…Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the U (1) standard model of electroweak…”
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Nonlinear Stability of Self-Gravitating Massive Fields by LeFloch, Philippe G., Ma, Yue

“…We consider the global evolution problem for Einstein’s field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field…”
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Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary by Giesselmann, Jan, LeFloch, Philippe G.

“…We study nonlinear hyperbolic conservation laws posed on a differential ( n + 1 ) -manifold with boundary referred to as a spacetime, and defined from a…”
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A Class of Mesh-Free Algorithms for Some Problems Arising in Finance and Machine Learning by LeFloch, Philippe G., Mercier, Jean-Marc

“…We introduce a numerical methodology, referred to as the transport-based mesh-free method , which allows us to deal with continuous, discrete, or statistical…”
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On the Global Evolution of Self-Gravitating Matter. Nonlinear Interactions in Gowdy Symmetry by Le Floch, Bruno, LeFloch, Philippe G.

“…We are interested in the evolution of a compressible fluid under its self-generated gravitational field. Assuming here Gowdy symmetry, we investigate the…”
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Boundedness of the conformal hyperboloidal energy for a wave-Klein–Gordon model by LeFloch, Philippe G., Oliver, Jesús, Tsutsumi, Yoshio

“…We consider the global evolution problem for a model which couples together a nonlinear wave equation and a nonlinear Klein–Gordon equation, and was introduced…”
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A structure-preserving algorithm for surface water flows with transport processes by Karjoun, Hasan, Beljadid, Abdelaziz, LeFloch, Philippe G.

“…We consider a system of coupled equations modeling a shallow water flow with solute transport and introduce an artificial dissipation in order to improve the…”
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Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes by Castro, Manuel J., LeFloch, Philippe G., Muñoz-Ruiz, María Luz, Parés, Carlos

“…We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics, and, for solutions containing shock waves, we investigate…”
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A Class of Well-Balanced Algorithms for Relativistic Fluids on a Schwarzschild Background by LeFloch, Philippe G., Parés, Carlos, Pimentel-García, Ernesto

“…For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms…”
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The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded by Dong, Shijie, LeFloch, Philippe G., Lei, Zhen

“…Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities…”
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