一类拟线性抛物方程解的性质

本文给出了一类拟线性抛物方程初边值问题的解的存在唯一性，本文还给出了解所满足的“能量”等式，从而证明了解关于时间变量的连续性。     

具有时滞的Rayleigh方程周期解的存在性与唯一性

本文研究了具有偏差变元的Rayleigh方程周期解的存在性和唯一性.利用Mawhin连续性定理,得到了该方程周期解存在性和唯一性的新结果,改进了一些已有结果.     

受迫二维广义KdV-Burgers方程的周期行波解

本文研究了受迫二维广义ＫｄＶ－Ｂｕｒｇｅｒｓ方程的周期行波解问题,讨论了解的有界性并给出了解的估计式,进而讨论了周期解的存在性及唯一性.     

具无穷时滞竞争扩散系统周期解的唯一性

研究了一类具有无穷时滞竞争扩散模型的周期解问题,采用了上下解的方法,获得了周期解的存在唯一性,并给出了解的渐近性态.     

二阶非线性椭圆偏微分方程Dirichlet问题的粘性解

研究了一类二阶非线性椭圆偏微分方程Dirichlet问题粘性解的存在性与唯一性。首先建立粘性解的比较定理，确保了解的唯一性，然后运用Perron方法构造出解。从而解决了这类问题的粘性解的存在性与唯一性。     

非Lipschitz条件下高维McKean-Vlasov随机微分方程解的存在唯一性

研究了一类漂移系数不连续的高维McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.在漂移系数关于空间变量逐段Lipschitz连续的条件下，首先利用Zvonkin变换将方程转换为漂移系数为Lipschitz连续的McKean-Vlasov随机微分方程，变换后的方程存在唯一解.然后由变换函数的性质可得逆函数的存在性和Lipschitz连续性.最后由It8公式及逆函数的性质可得原来的McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.     

具有时滞的非线性微分方程的概周期解的存在性及唯一性

本文研究了一类具有时滞的非线性微分方程的有界解及概周期解的存在性及唯一性问题。利用变量替换和不动点方法及逼近法,我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。我们的结果大大改进和推广了文［２］的主要结果。     

一类带修理工休假可修系统解的存在唯一性及正则性分析

考虑一类修理工可多重延误休假的n部件串联可修复系统解的存在唯一性及正则性问题.通过将系统模型方程转化为一组算子积分方程,利用不动点理论讨论该系统局部解的存在唯一性问题,再由一致先验估计和连续延拓讨论系统整体解的存在唯一性问题,继而分析解的正则性问题.为解决复杂可修复系统解的存在唯一性及正则性提供了可行性方法,并且方法同样适用于排队论系统和其他类似系统.     

Benjamin-Ono方程的广义解

讨论了Benjamin-Ono方程在Colombeau意义下的广义解的存在性，唯一性及在经典解存在的情况下与经典解的关系．     

一类带积分边界条件的三阶微分方程边值问题的解

运用Banach压缩映射原理以及Leray-Schauder连续性原理,在非线性项为L1-Caratheodory函数的条件下,研究了一类带积分边界条件的三阶微分方程边值问题解的唯一性、存在性以及解集的紧性.     

Mathematical analysis of a three-dimensional eutrophication model

In this paper we present and analyze a nutrient-phytoplankton-zooplankton-organic detritus-dissolved oxygen mathematical model simulating eutrophication processes into aquatic media. As a main result, we obtain existence and uniqueness results for the solution of the system, under realistic hypotheses of non-smooth coefficients (in particular, a non-regular water velocity). This lack or regularity prevent us from using the standard semigroup approach, forcing us towards the utilization of more refined techniques.     

A free boundary tumor model with time dependent nutritional supply

A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equation describing the evolution of the tumor size. First the global existence and uniqueness of a transient solution is established under some general conditions. Then with additional regularity assumptions on the consumption and proliferation rates, the existence and uniqueness of steady-state solutions is obtained. Furthermore the convergence of the transient solutions toward the steady-state solution is verified. Finally the long time behavior of the solutions is investigated by transforming the time-dependent domain to a fixed domain.     

Evolutionary Boussinesq model with nonmonotone friction and heat flux boundary conditions

In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time retardation and regularization technique, combined with a regularized Galerkin method, and recent results from the theory of hemivariational inequalities.     

Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint

The existence and regularity of the solution for the fully nonlinear second order elliptic equation with gradient constraint are discussed in this paper. We prove the existence of the strong solution by choice of special penalty function, and obtain the local W^{2,∞} estimate of the solution by means of the theory of viscosity solution with the auxiliary function method.     

The solution of transonic flow problems by the method of stabilization

The paper deals with the study of the perturbated Full Potential Equation. The proofs of existence, unicity and regularity of the solution are given. The main result consists in the fact that the resulting strong solution is the generic solution for the Transonic Flow Problem     

On the global existence and small dissipation limit for generalized dissipative Zakharov system

This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.     

中立型时滞Lotka-Volterra系统正周期解的存在性

本文研究了具有m个捕食者n个食饵的中立型时滞Lotka-Volterra系统,并 利用重合度理论中的连续性引理,得到了该系统正周期解存在性的充分条件.     

The phase-field transition system with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity

The paper establishes the existence, estimate, uniqueness and regularity for the solution of a nonlinear parabolic system (a two-phase Caginalp type system) with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity. It extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena, including phase separation.     

Classical Solution to the Electropainting Problem

The mathematical modelling of the electrodeposition phenomenon leads to a linear elliptic partial differential equation subject to nonlinear evolutionary mixed boundary conditions. ln this paper, the existence, uniqueness and regularity of classical solution are proved for the electropainting problem when “dissolution current” is zero.