Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Huo, Xiaokai"'
Autor:
Huo, Xiaokai, Liu, Hailiang
Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen the emerge
Externí odkaz:
http://arxiv.org/abs/2401.17233
This article shows how to combine the relative entropy method by D. Bresch, P.-E. Jabin, and Z. Wang in arXiv:1706.09564, arXiv:1906.04093 and the regularized $L^2(\mathbb{R}^d)$-estimate by Oelschl\"ager (Probability theory and related fields, 1987)
Externí odkaz:
http://arxiv.org/abs/2311.01980
Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting. However, existi
Externí odkaz:
http://arxiv.org/abs/2310.10767
Autor:
Huo, Xiaokai, Jüngel, Ansgar
A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier-Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration
Externí odkaz:
http://arxiv.org/abs/2307.03412
This paper is devoted to the diffusive limit of the nonlinear radiative heat transfer system with curved boundary domain (\textit{two dimensional disk}). The solution constructed in \cite{ghattassi2022convergence} by the leading order interior soluti
Externí odkaz:
http://arxiv.org/abs/2305.17661
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using asymptoti
Externí odkaz:
http://arxiv.org/abs/2210.16681
This paper focuses on the nonlinear Milne problem of the radiative heat transfer system on the half-space. The nonlinear model is described by a second order ODE for temperature coupled to transport equation for radiative intensity. The nonlinearity
Externí odkaz:
http://arxiv.org/abs/2207.10769
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded dom
Externí odkaz:
http://arxiv.org/abs/2205.06478
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the proofs are
Externí odkaz:
http://arxiv.org/abs/2110.05331
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions
Externí odkaz:
http://arxiv.org/abs/2007.13209