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pro vyhledávání: '"Golse, Francois"'
We present a simple model in dimension $d\geq 2$ for slowing particles in random media, where point particles move in straight lines among and inside spherical identical obstacles with Poisson distributed centres. When crossing an obstacle, a particl
Externí odkaz:
http://arxiv.org/abs/2406.05895
Autor:
Filbet, Francis, Golse, François
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by applying a
Externí odkaz:
http://arxiv.org/abs/2405.13436
A half-space problem of a linear kinetic equation for gas molecules physisorbed close to a solid surface, relevant to a kinetic model of gas-surface interactions and derived by Aoki et al. [K.~Aoki et al., in: Phys. Rev. E 106:035306, 2022], is consi
Externí odkaz:
http://arxiv.org/abs/2404.09099
We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension at most $\frac{|\gamma+2s|}{2s}$ with $\gamma \in [-4s,-2s)$ and $s \i
Externí odkaz:
http://arxiv.org/abs/2312.11079
Autor:
Golse, François
Obtaining a rigorous justification of the kinetic theory of gases from Newton's second law of dynamics for a large number of identical spheres interacting by elastic binary collisions, is a problem formulated by Hilbert in 1900 (Hilbert's 6th problem
Externí odkaz:
http://arxiv.org/abs/2308.11919
Autor:
Golse, François
This text is a set of lecture notes for a 4.5-hour course given at the Erd\"os Center (R\'enyi Institute, Budapest) during the Summer School "Optimal Transport on Quantum Structures" (September 19th-23rd, 2023). Lecture I introduces the quantum analo
Externí odkaz:
http://arxiv.org/abs/2308.11134
Autor:
Golse, François
This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent $p\in[1,+\infty)$ in the case of a general Polish space. In particular it avoids the "glueing of couplings" pr
Externí odkaz:
http://arxiv.org/abs/2308.03133
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations (PDEs), l
Externí odkaz:
http://arxiv.org/abs/2209.11220
To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a
Externí odkaz:
http://arxiv.org/abs/2208.06410
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix given by the convolution product of the solution with the matrix $a_{
Externí odkaz:
http://arxiv.org/abs/2206.05155