A dyadic decomposition approach to a finitely degenerate hyperbolic problem

退化抛物方程——解的紧性与正则性

Degenerate parabolic equations -- compactness and regularity of solutions

本文提出一种新方法，通过动力学公式化约化，解决了退化抛物方程熵解的正则性与紧性问题，并证明了非齐次情形弱解的存在性。

Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation

This paper is concerned with existence and multiplicity results for the semilinear subelliptic equation with free perturbation term. By using the degenerate Rellich-Kondrachov compact embedding theorem, precise lower bound estimates of Dirichlet eigenvalues for the finitely degenerate elliptic operator and minimax method, we obtain the existence and multiplicity of weak solutions for the problem.

有限应变固体完全熔化为粘弹性流体的斯蒂芬问题

The Stefan problem for complete melting of finitely strained solids into viscoelastic fluids

研究有限应变固体完全熔化为粘弹性流体的斯蒂芬问题，在欧拉框架大应变下建模，采用杰弗里斯流变学，通过纳入动力学过热和过冷扩展经典问题，利用多极非简单连续统概念及时间离散分析求解。

Variational Inequalities of Navier--Stokes Type with Time Dependent Constraints

We consider a class of parabolic variational inequalities with time dependent obstacle of the form $|{\boldsymbol u}(x,t)| \le p(x,t)$, where ${\boldsymbol u}$ is the velocity field of a fluid governed by the Navier--Stokes variational inequality. The obstacle function $p=p(x,t)$ imposed on ${\boldsymbol u}$ consists of three parts which are respectively the degenerate part $p(x,t)=0$, the finitely positive part $0< p(x,t) <\infty$ and singular part $p(x,t)=\infty$. In this paper, we shall propose a sequence of approximate obstacle problems with everywhere finitely positive obstacles and prove…

关于等距浸入的退化Weyl问题

On the degenerate Weyl problem on isometric immersions

本文研究二维球面等距浸入的退化Weyl问题，在仅非负高斯曲率条件下，分别给出了全局$C^{2,1}$嵌入和$W^{3,p}$浸入的存在性结果，并解决了非退化情形。

非线性双曲系统：非退化通量、内部速度变化与图解

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

针对一般非线性严格双曲系统，提出非退化条件确保黎曼问题仅有有限波，引入内部速度变化概念推导新的相互作用估计，设计波前追踪方案并证明强收敛到熵解，应用于图解的时间正则性。