Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations

The uniqueness and existence of BV-solutions for Cauchy problem of the form are proved.

Uniqueness and stability of solutions for Cauchy problem of nonlinear diffusion equations

The uniqueness of solutions for Cauchy problem of the formis studied.It is proved that if u ∈BVx and A(u) is strictly increasing,the solution is unique.

SOURCE－TYPE SOLUTIONS OF A QUASILINEAR DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

The existence and nonexistence of non-trivial solutions for the Cauchy problem of the formare studied.

多维拟线性退化抛物方程Cauchy问题解的唯一性和稳定性

本文证明了拟线性退化抛物方程■的Cauchy问题BV解的唯一性和稳定性.

二阶退化双曲型方程的Cauchy问题(英文)

讨论退化秩为0的二阶双曲型方程的Cauchy问题,主要证明了此问题解的存在性和唯一性.

拟线性退化抛物方程Cauchy问题的解

对来自金融数学领域的方程_(xx)u+u_yu-_tu=c(x,y,t,u),(x,y,t)∈Q_T=R^2×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质.

一类非线性退缩抛物方程的Cauchy问题

讨论带吸收项的非线性双重退缩抛物方程ut =div(| um|p-2 um) -uq 具有初值u(x ,0 ) =μ∈L∞loc(RN)的Cauchy问题 .利用正则化方法 ,首先得到了正则化问题非负古典解的一致估计 ,最后在初值满足一定的增长条件下 ,证明了双重退缩抛物方程Cauchy问题弱解的存在性与不存在性 .

一个拟线性退化抛物方程Cauchy问题解的存在性

利用人工粘性法构造一个特殊的拟线性退化抛物方程Cauchy问题的粘性解,最后得到弱解的存在存在性。

具可测系数的一类拟线性退化抛物方程的局部化条件

使用Ｍｏｓｅｒ迭代技巧和Ｓｏｂｏｌｅｖ嵌入定理，研究了方程ｕｔ＝（ａｉｊ（ｘ，ｔ）｜ｕ｜ｐ－２ｕｘｉ）ｘｊ－ｕｑ具有初始条件ｕ（ｘ，０）＝ｕ０（ｘ）的Ｃａｕｃｈｙ问题解的局部化条件。

N维扩散方程解的界面性态估计

本文考察N维空间中—类退化扩散方程Cauchy问题解的界面性态,通过构造一类函数利用比较原理,得到了解的界面性态估计.

非自治退化抛物-双曲方程的柯西问题

非自治退化抛物-双曲型方程可以描述许多自然现象.主要研究这类方程的柯西问题,建立了动力学公式,在对流函数、扩散函数适当光滑性的基础上,证明了该问题动力学解的存在唯一性.

两个拟线性退化抛物型方程柯西问题弱解存在性的同一种求解方法

先构造一个压缩算子半群,后用此压缩算子半群分别去求解如下两个齐次与非齐次的拟线性退化抛物型方程的柯西问题的弱解存在性:{?u/?t-ΔΦ(u)=0(x,t)∈R^n×R^+ u(x,0)=u_0(x)x∈R ~n{?u/?t-ΔΦ(u)=f(x,t)(x,t)∈R^n×R^+ u(x,0)=0 x∈R^n其中:Δ为拉普拉斯算子,Φ(s)∈C^2(R),Φ(0)=0,Φ′(s)≥0,且集合{s∈R|Φ′(s)=0}不含有内点.

Qualitative analysis and simulation of a nonlinear integro-differential system modeling tumor-immune cells competition

This paper deals with a qualitative and computational study of a class of integrodifferential model, with a nonlinear growth rate. The model is applied to immunology problems, in particular to the competition between tumors and immune system. Our purpose is to take into account the activity transfer processes bet ween cells. The first part of this paper deals with the modeling, while the second part develops the existence and uniqueness of global solutions to the initial boundary value problem related to the application of the model. Finally, numerical simulations are used to illustrate the results obtained for a dynamic of tumor cells contrasted by the immune system.