An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems

具有广义扩散和逻辑源的Keller-Segel方程的有界弱解：基于非平衡最优输运分裂格式

Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme

针对具有广义扩散和逻辑源的抛物-椭圆型Keller-Segel方程，在齐次Neumann边界条件下，通过非平衡最优输运框架构造了全局有界弱解，并量化了趋化敏感性与降解参数及初始密度界的关系。

平流-超扩散方程的下界

Lower Bounds for the Advection-Hyperdiffusion Equation

研究二维和三维全空间平流-超扩散方程解的衰减行为，将平流项视为扰动，结合Fourier分裂方法与经典PDE技术，通过插值得到H^{-1}范数的下界。

适定主动标量方程的算子分裂

Operator splitting for well-posed active scalar equations

针对非线性平流与线性扩散/色散耦合的主动标量方程，证明了Godunov和Strang分裂方法在初始数据足够正则时具有预期收敛阶。

Lower bounds on mixing norms for the advection diffusion equation in $\mathbb{R}^d$

An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in $\mathbb{R}^d$ with $d=2,3$ is derived using the Fourier splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a lower bound on the $L^2-$ norm of the inverse gradient of the solution is obtained via gradient estimates and interpolation.

Splitting-based domain decomposition methods for two-phase flow with different rock types

In this paper, we are concerned with the global pressure formulation of immiscible incompressible two-phase flow between different rock types. We develop for this problem two robust schemes based on domain decomposition (DD) methods and operator-splitting techniques. The first scheme follows a sequential procedure in which the (global) pressure, the saturation-advection and the saturation-diffusion problems are fully decoupled. In this scheme, each problem is treated individually using various DD approaches and specialized numerical methods. The coupling between the different problems is expli…

A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case…