Analyzability in the context of PDEs and applications

全空间上的保守随机偏微分方程

Conservative stochastic PDEs on the whole space

本文为全空间上的保守随机偏微分方程建立适定性理论，涵盖带相关噪声的Dean--Kawasaki方程，并严格化零程粒子过程中涨落流体力学与宏观涨落理论的联系。

变分原理及其在对称偏微分方程中的应用

Variational principles and aplications to symmetric PDEs

本文在群不变映射框架下探讨了Ekeland变分原理的多种等价形式，推广了Drop和Petal等定理，并将其应用于偏微分方程的Plateau问题、控制理论及Pontryagin最大值原理的扩展。

Spencer delta-cohomology, restrictions, characteristics and involutive symbolic PDEs

We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results due to Guillemin and Quillen relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context, though in a modified form. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating Spencer delta-cohomology of a symbolic system and its restriction to a non-characteristic subspace.

Wasserstein空间上BSDE的概念及其在控制问题和PDEs中的应用

A notion of BSDE on the Wasserstein space and its applications to control problems and PDEs

本文引入了Wasserstein空间上的BSDE新概念，将其推广至平均场设定，并证明其与平均场控制问题和PDEs的对应关系，建立了比较原理与存在性结果。

Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs

This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduced in \cite{EKTZ} which considers as test functions all those smooth processes which are tangent in mean. When restricted to the Markovian case, this definition induces a larger set of test functions, and reduces to the notion of stochastic viscosity solutions analyzed in \cite{BayraktarSirbu1,BayraktarSirbu2}. Our main result takes advantage of this enlargement of the test functions, and provides an easier proof of …

反问题研究：建模电解槽的准线性椭圆系统

Inverse problems for quasi-linear elliptic systems modeling electrolysers

本文研究电解槽中电化学过程的反问题，通过耦合的准线性椭圆PDE系统，探讨如何利用边界和内部测量数据唯一重建非线性扩散系数和电势关系。