Zobrazeno 1 - 10
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pro vyhledávání: '"Carrillo, Jose A"'
We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space $\bbh^\dm$. The free energy consists of two competing terms: an entropy, correspondin
Externí odkaz:
http://arxiv.org/abs/2409.06022
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the tensorized law of
Externí odkaz:
http://arxiv.org/abs/2408.15035
Autor:
Carrillo, José Antonio, Lin, Ke
The qualitative study of solutions to the coupled parabolic-elliptic chemotaxis system with nonlinear diffusion for two species will be considered in the whole Euclidean space $\mathbb{R}^d$ ($d\geq 3$). It was proven in \cite{CK2021-ANA} that there
Externí odkaz:
http://arxiv.org/abs/2408.13992
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs by regula
Externí odkaz:
http://arxiv.org/abs/2408.02345
The dynamics of probability density functions has been extensively studied in science and engineering to understand physical phenomena and facilitate algorithmic design. Of particular interest are dynamics that can be formulated as gradient flows of
Externí odkaz:
http://arxiv.org/abs/2407.15693
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor positive (semi
Externí odkaz:
http://arxiv.org/abs/2406.09227
This is a survey article based on the content of the plenary lecture given by Jos\'e A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and appl
Externí odkaz:
http://arxiv.org/abs/2405.16679
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combi
Externí odkaz:
http://arxiv.org/abs/2405.00891
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain $\Omega \subset \mathbb{R}^{d}$, where $d = 2$ or $3$. The pressure in the model is defined as the sol
Externí odkaz:
http://arxiv.org/abs/2404.18901
Publikováno v:
Communications in Mathematical Analysis and Applications 3(2), 266-286 (2024)
In this work we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical challenge
Externí odkaz:
http://arxiv.org/abs/2404.18108