On the diffusive stress relaxation for multidimensional viscoelasticity

Relative entropy in diffusive relaxation

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate-type.

多维守恒律的非线性扩散-色散极限

Nonlinear diffusive-dispersive limits for multidimensional conservation laws

研究具有消失非线性扩散和色散项的多维守恒律，在扩散与色散系数相对大小条件下，证明扩散-色散解在Lp空间中一致有界并收敛到经典熵解。

Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance: time-delayed, standard diffusive (which includes the Riemann-Liouville fractional integral) and extended diffusive (which includes the Caputo fractional derivative). The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a dissipative realization of the impedance operator, be it finite or infinite-dimensional. The a…

一种无扩散的多层神经网络方法用于多维非线性双曲方程

A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations

本文提出LeafNet算法，通过重写守恒律系统并利用物理信息算法逼近光滑解，实现多维非线性双曲方程的无扩散计算，并给出误差分析与二维实验验证。