Workshop on homogenization theory and related applications

November 8th-9th, 2025  MCM110  

Invited Speakers

Organizers

Prof. Weiwei Ding (South China Normal Univ) 

Bistable pulsating fronts in one-dimensional slowly oscillating environments

In this talk, I will present some progress on reaction-diffusion fronts in spatially periodic bistable media. The results include: existence of pulsating fronts with large periods, existence of and an explicit formula for the limit of front speeds as the spatial period goes to infinity, convergence of pulsating front profiles to a family of front profiles associated with spatially homogeneous equations. This talk is based on joint work with Francois Hamel and Xing Liang.

Prof. Chenlin Gu (YMSC)

Relaxation to equilibrium of non-gradient exclusion processes

For the conservative particle systems in infinite volume, the relaxation to equilibrium is expected to be a Gaussian-type decay. The sharp decay rate was known for two models - SSEP by Bertini and Zegarlinski, and zero-range processes by Janvresse, Landim, Quastel and Yau - and they are obtained via different methods. This talk aims to unify the two existing approaches with homogenization, and presents the result in speed-change exclusion processes. The talk is based on a joint work with Linzhi Yang.

Prof. Wenjia Jing (YMSC)

Dynamics of wave packets near a Dirac point in the subwavelength regime

It is known that Dirac dispersion cones exist at subwavelength scales in bubbly honeycomb phononic crystals. In this talk we will present the time-evolution of wave packets that are spectrally concentrated near such a Dirac point. It turns out that the wave packets remain spectrally close to the Dirac point while the envelopes evolve according to a 2D Dirac system up to a long time. The subwavelength scale affects the description naturally. The talk is based on a joint work with H. Ammari and X. Fu.

Prof. Yong Lu (Nanjing Univ)

Qualitative/quantitative homogenization of some non-Newtonian flows in perforated domains

We consider the homogenization of stationary and evolutionary  incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains perforated with a large number of periodically distributed small holes in $R^{3}$,  where the mutual distance between the holes is measured by a small parameter $\epsilon>0$ and the size of the holes is $\epsilon^{\alpha}$ with $\alpha \in (1, \frac 32)$. The Darcy's law is recovered in the limit. Instead of using their restriction operator to derive the estimates of the pressure extension by duality, we use the Bogovskii type operator in perforated domains to deduce the uniform estimates of the pressure directly. Moreover, quantitative convergence rates are given.  This is a joint work with F. Oschmann and R. Hofer.

Dr. Bojing Shi (USTC)

Quantitative estimates in almost periodic homogenization of parabolic systems

In this talk, I will present our recent work for a family of second order parabolic operators in   divergence form with rapidly oscillating and almost-periodic coefficients. We establish uniform interior and boundary Hölder and Lipschitz estimates as well as convergence rate. The estimates of fundamental solution and Green's function are also obtained. This talk is based on a joint work with Professor Jun Geng.

Prof. Bian Wu (Max Planck Institute)

On anomalous dissipation and Euler flows

Anomalous dissipation is a central postulate in Kolmogorov-Obukhov–Corrsin theory of hydrodynamic turbulence. I will discuss how to prove this postulate for scalar fields in ideal turbulence, using convex integration and homogenization theory. This is a joint work with Jan Burczak and László Székelyhidi.

Prof. Qiang Xu (Lanzhou Univ)

Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law

In this talk, focusing on Darcy’s law incorporating memory effects, we plan to introduce non-stationary Stokes equations on perforated domains, and state a sharp homogenization error for both velocity and pressure in terms of the energy norm. Except of gauging the boundary layers induced by the incompressibility condition, a significant difficulty arises from the incompatibility between initial and boundary values in the corrector's equation, and we present a methodology which hold a great potential for tackling the same issue in other evolutionary models beyond a homogenization setting. This work is cooperated with Li Wang and Zhifei Zhang.

Prof. Yao Xu (UCAS)

Optimal convergence rates in multiscale elliptic homogenization

In this talk, we present our recent work on the quantitative periodic homogenization of multiscale elliptic operators. Under the assumption of real analytic coefficients, we introduce the so-called multiscale correctors and more accurate effective operators. This helps improve the ratio part of the convergence rate to an exponential one, which is optimal in our setting. Based on this result, we also establish the uniform Lipschitz estimate under a mild double-log scale-separation condition. This is a joint work with Weisheng Niu and Jinping Zhuge.

Prof. Weijun Xu (BICMR)

Periodic homogenisation for singular stochastic PDEs

We will introduce renormalisation procedures in recent developments in singular stochastic PDEs, as well as homogenisation problem for equations with oscillatory coefficients. Both renormalisation and homogenisation are singular limiting procedures, but with very different features. It is then natural to ask how these two limiting procedures interact with each other when present in the same problem. We will also share some of our recent works and understandings in this direction. Part of the talk are based on joint works with Yilin Chen and Ben Fehrman.

Prof. Lei Zhang (Shanghai Jiao Tong Univ)

Numerical Homogenization: A Personal Overview and Analysis Questions

Numerical homogenization addresses the challenge of constructing finite-dimensional approximations for the solution spaces of PDEs with rough coefficients, such as divergence-form elliptic equations with L^\infty coefficients. Conventional methods, like standard finite elements, can perform arbitrarily badly for PDEs with rough coefficients. While some approaches in numerical homogenization build on classical concepts like periodic homogenization and scale separation, a key objective of numerical homogenizaiton is to handle arbitrarily rough coefficients in the absence of scale separation. This talk will offer a brief personal overview on numerical homogenization, addressing both scale-separated and non-separable cases. I will conclude by presenting open analysis questions (to my knowledge) from my research in periodic, quasi-periodic, and non-separable scale settings.

Prof. Jianlu Zhang (AMSS, CAS)

Convergence rate of homogenization for quasi-periodic Hamilton-Jacobi equations

In 1987, Lions firstly proposed the homogenization for Hamilton-Jacobi equations, which revealed the significance of effective Hamiltonian in controlling the large time behavior of solutions. The quantitative estimate of such a homogenization was studied in recent years, which mainly answers the convergence rate for compact case. In this talk, we will introduce a novel quasi-periodic approach, which reveals the relation between the smoothness of effective Hamiltonian and the convergence rate.

Note:

There is no registration fee for this conference.

If you have any other questions, please send email to us (mcmoffice@math.ac.cn).