A system of state-dependent delay differential equation modelling forest growth II: boundedness of solutions

具有无界粘性的湍流系统的结果：弱形式，解的存在性，有界性，光滑性

Results for a turbulent system with unbounded viscosities: weak formulations, existence of solutions, boundedness, smoothness'

我们考虑一个循环系统中出现的湍流模型在流体动力学与无界涡粘性。各种概念的弱解被认为是和比较。我们建立了存在性和正则性结果。特别地，我们研究了弱解的有界性。我们还建立了一个经典解的存在性结果

Global boundedness and decay property of a three-dimensional Keller--Segel--Stokes system modeling coral fertilization

This paper is concerned with the four-component Keller--Segel--Stokes system modelling the fertilization process of corals: \begin{equation*} \left\{ \begin{array}{ll} ρ_t+u\cdot\nablaρ=Δρ-\nabla\cdot(ρ\mathcal{S}(x,ρ,c)\nabla c)-ρm, & \quad (x,t)\in Ω\times (0,T), \\ m_t+u\cdot\nabla m=Δm-ρm, & \quad (x,t)\in Ω\times (0,T), \\ c_t+u\cdot\nabla c=Δc-c+m, & \quad (x,t)\in Ω\times (0,T), \\ u_t=Δu-\nabla P+(ρ+m)\nablaϕ,\quad \nabla\cdot u=0, & \quad (x,t)\in Ω\times (0,T) \end{array}\right. \end{equation*} subject to the boundary conditions $\nabla c\cdot ν=\nabla m\cdot ν=(\nablaρ-ρ\mathcal{S}(…

模拟生物膜生长的奇异与退化演化系统的鲁棒时间离散化和线性化格式

Robust time-discretisation and linearisation schemes for singular and degenerate evolution systems modelling biofilm growth

本文针对模拟生物膜生长的拟线性退化演化方程组，提出半隐式时间离散与迭代线性化格式，证明其正性、有界性和收敛性，并通过有限元数值实验验证其鲁棒性和高效性。

与非线性微分方程耦合的椭圆型变分不等式的弱可解性

Weak solvability of elliptic variational inequalities coupled with a nonlinear differential equation

本文研究与非线性常微分方程耦合的椭圆型变分不等式，利用迭代逼近格式和改进的 Moser 迭代获得一致先验界，证明解的存在性、唯一性与有界性，并去除粘接强度需预先有界的限制。

Comparison principles and applications to mathematical modelling of vegetal meta-communities

This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the fragmentation of the habitat on biodiversity. A simple neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within ea…