Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem without Monotonicity Condition

具有一个受控状态的三个互联半线性反应扩散PDE的内部镇定

Internal stabilization of three interconnected semilinear reaction-diffusion PDEs with one actuated state

本文研究三个互联半线性反应扩散PDE系统的欠驱动内部指数镇定问题，采用模态分解、目标系统变换与高增益方法设计静态线性比例状态反馈控制器，并通过Lyapunov分析导出保证任意衰减率指数稳定且始终可行的LMI条件。

具有相互连接障碍的偏微分方程组的粘性解与多模式切换问题

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

本文通过斜反射反射BSDE系统，证明了具有相互连接障碍的m个变分偏微分不等式系统在粘性意义下的解的存在唯一性，并应用于能源市场中发电厂的估值问题。

Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs. Then we show by means of classical maximum principles that nonlinear parabolic equations with boundary disturbances are monotone control systems. With these two facts, we establish that ISS of the original nonlinear parabolic PDE with constant \textit{boundary disturbances} is equivalent to ISS of a closely related nonlinear parabolic PDE with constant \tex…

基于正则化方法的PDE系统中参数变化的支撑集识别

Support identification for parameter variations in a PDE system via regularized methods

研究从边界测量恢复PDE系统中参数变化空间支撑集的逆问题，提出结合单调性原理与TSVD正则化的混合方法，提升了重构精度、噪声鲁棒性与支撑集定位锐度，数值实验验证了其有效性。

Input-to-State Stability of Nonlinear Parabolic PDEs with Dirichlet Boundary Disturbances

We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs. Then we show by means of classical maximum principles that nonlinear parabolic equations with boundary disturbances are monotone control systems. With these two facts, we establish that ISS of the original nonlinear parabolic PDE with constant boundary disturbances is equivalent to ISS of a closely related nonlinear parabolic PDE with constant distributed d…

Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data

In this paper we study second order master equations arising from mean field games with common noise over arbitrary time duration. A classical solution typically requires the monotonicity condition (or small time duration) and sufficiently smooth data. While keeping the monotonicity condition, our goal is to relax the regularity of the data, which is an open problem in the literature. In particular, we do not require any differentiability in terms of the measures, which prevents us from obtaining classical solutions. We shall propose three weaker notions of solutions, named as {\it good soluti…