Preface: 70 Years Break Forward, Build on the Momentum, and Work Together for a New Chapter (Part I)

On the Kernel of the Borel's Characteristic Map of Lie Groups
Haibao Duan & Xuezhi Zhao

Convergence Rate of Solutions to a Hyperbolic Equation with p(x)-Laplacian Operator and Non-Autonomous Damping
Wenjie Gao, Xiaolei Li & Chunpeng Wang

On a Class of Quasilinear Elliptic Equations
Sayed Hamid Hashimi, Zhi-Qiang Wang & Lin Zhang

Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation
Liang-Wei Wang, Shu-Ying Wang, Jingxue Yin & Zheng-Wen Tu

Operators on Sobolev Type Spaces
Guangfu Cao & Li He 

Advance in Operator Theory and Jiang's Seven Questions
Chunlan Jiang & Yang Cao 

A Structure-Preserving Numerical Method for the Fourth-Order Geometric Evolution Equations for Planar Curves
Eiji Miyazaki, Tomoya Kemmochi, Tomohiro Sogabe & Shao-Liang Zhang