退缩抛物型方程解的熄灭时间

证明了一类退缩抛物型方程解在有限时刻熄灭,并对解的熄灭时间进行估计     

抛物型方程解的一个性质

本文考虑无界区域上形如(1)的抛物型方程的解在|x|~2 t←∞时的增长性质,推广了[1]中对椭圆型方程的解得到的类似结果。     

半无界空间上退缩抛物型方程解的存在性与爆破

讨论半无界空间上退缩抛物型方程解的存在性与爆破性质.证明了在小初值时解是全局存在的,在大初值时局部解在有限时刻发生爆破.     

双非线性抛物型方程非负解的一个性质

在Ｅ＾ｎ（０，∞）上讨论双非线性抛物型方程ａ／ａｔ（｜ｕ｜＾λ－２ｕ）－ｄｉｖ（｜△ｕ｜＾ｐ－２△ｕ）＝０在ｐ＞λ＞２的条件下，证明它的齐次Ｃａｕｃｈｙ问题非负整体解必是零解。     

具有双障碍的退缩抛物变分不等式解的存在性和唯一性

本文研究具有双障碍的退缩抛物变分不等式，我们利用罚技巧，有限逼近和先验估计方法，得到一类退缩抛物变分不等式弱解的存在性，并在一定条件下，建立了弱解的唯一性。本文结论对广泛的一类抛物物型变分不等式成立。     

一类拟线性退缩抛物型方程整体解的存在性与衰减估计

本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减估计.所得结果改进并推广了文献[1]的相应结果.     

Blow Up for Solutions of Nonlinear Doubly Degenerate Parabolic Equation

Ｂｌｏｗ　Ｕｐ　ｆｏｒ　Ｓｏｌｕｔｉｏｎｓ　ｏｆ　Ｎｏｎｌｉｎｅａｒ　Ｄｏｕｂｌｙ　Ｄｅｇｅｎｅｒａｔｅ　Ｐａｒａｂｏｌｉｃ　ＥｑｕａｔｉｏｎＢｌｏｗＵｐｆｏｒＳｏｌｕｔｉｏｎｓｏｆＮｏｎｌｉｎｅａｒＤｏｕｂｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃ...     

A Nonlinear Degenerate Parabolic Equation

ＡＮｏｎｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎ￥ＪｉａｎｇＹｉｎｇｊｉｅ（ＪｉａｏｚｕｏＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｓｔｕｄｙａｎｏｎｌｉｎｅｒｄｅｇｅｎｅｒａｔｅｐａｒａｂｏｌｉｃｅ...     

拟线性抛物方程的弱解

该文给出了拟线性退化抛物方程pa_t{u}+pa_x{f(u)}=pa_xx{A(u(x,t))}∈R^2_+×(0,+∞) ,u(x,0)=u_0(x),x∈R 一种弱解的新定义, 利用Div Curl引理证明了解的存在性．     

Source Type Solutions of a Fourth Order Degenerate Parabolic Equation

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 〈 n 〈 2p - 1 and has no solution of this type if n ≥ 2p - 1.     

Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q ＞ 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n 1)/ m 1}.     

一类具有非线性内部源和边界流的双重退化抛物型方程

This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q ＞ 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n 1)/ m 1}.     

Properties on Interface of Solutions for a Doubly Degenerate Parabolic Equation

We investigate the properties of the interface of the solution for a doubly nonlinear degenerate parabolic equation and show that the interface is nondecreasing and Lipschitz continuous.     

Regularity Results for a Strongly Degenerate Parabolic Equation

M. Bertsch & R. Dal Passo proved the existence and uniqueness of the Cauchy problem for u_t = (φ(u),ψ(u_x))_x, where φ > 0, ψ is a strictly increasing function with lim_{s → ∞}ψ(s) = ψ_∞ < ∞. The regularity of the solution has been obtained under the condition φ" < 0 or φ = const. In the present paper, under the condition φ" ≤ 0, we give some regularity results. We show that the solution can be classical after a finite time. Further, under the condition φ" ≤ -α_0 (where -α_0 is a constant), we prove the gradient of the solution converges to zero uniformly with respect to x as t → +∞.     

二阶拟线性退化抛物方程Cauchy问题解的稳定性

在一定的结构性条件下,证明了如下形式的拟线性退化抛物方程 Cauchy问题解的稳定性．     

一类双重退化抛物方程局部解的存在性

This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate p- Laplace equation(p＞2) u_t-div(b(x,t,u)|▽u|~(p-2)▽u)=f(x,u,t). The initial-boundary value problem in a bounded domain of R~N is considered under mixed boundary conditions.The existence of local-in-time weak solutions is obtained.