非局部的退化抛物型方程组解的整体存在与爆破条件

利用正则化技术和上下解方法,研究一类非局部的退化抛物型方程组,确定解的局部存在性、整体存在性与爆破条件.     

有非局部源退化抛物方程组解的爆破

本文讨论一类具有非局部源退化抛物方程组．通过利用上下解方法得到解的全局存在和有限时刻爆破，给出爆破集是整个区域，而且得到了解的爆破率．     

非局部退化拟线性抛物型方程组解的爆破和整体存在性

该文采用弱上下解方法和正则化技巧,研究了一类非局部退化抛物型方程组解的爆破和整体存在性,给出了爆破指标,并对非退化情形m=n=1,p_1=q_1=0,p_2q_21给出了一致爆破速率.     

非局部边界条件的退化抛物方程组解的爆破和整体存在性

主要讨论具有非局部源与非局部边界条件的退化抛物型方程组,借助于上解与下解的技术,给出了该系统整体解的存在与有限时刻爆破的条件.此结果不仅扩充了已有的结论~([8]),而且表明,系数a,b和边界条件中的权重函数g_1(x,y),g_2(x,y),以及常数l_1,l_2在决定系统解的爆破与否中起着关键的作用.     

具有非局部源的退化半线性抛物型方程组解的爆破

本文讨论具有非局部源退化半线性抛物型方程组的初边值问题 .证明了局部解的存在唯一性并且得到当初值充分大时解在有限时刻爆破 .     

带非局部源的退化奇异半线性抛物方程的爆破

本文研究带齐次Dirichlet边界条件的非局部退化奇异半线性抛物方程ut-(xαux)x=∫0af(u)dx在(0,a)×(0,T)内正解的爆破性质,建立了古典解的局部存在性与唯一性.在适当的假设条件下,得到了正解的整体存在性与有限时刻爆破的结论.本文还证明了爆破点集是整个区域,这与局部源情形不同.进而,对于特殊情形:f(u)=up,p>1及,f(u)=eu,精确地确定了爆破的速率.     

源项耦合的退化抛物型方程组解的爆破和整体存在

本文研究了一类描述可燃混合气体的热传播过程理论的退化抛物型方程组.借助于椭圆问题的特征值与特征函数理论,通过构造不同的上、下解得到了方程组解的整体存在与有限时刻爆破的条件.此结果不仅扩充了只讨论两个函数的半线性问题,并且证明了方程组中的系数ai,边界条件中的权重函数gi(x,y)以及指数li在决定问题解的爆破与否中起着关键的作用.     

具非局部源退化抛物型方程组的一致爆破模式

考虑带有齐次Dirichlet边界条件且具有非局部源项的退化抛物型方程组正解的爆破性质. 在适当条件下, 建立了该问题解的局部存在性并证明解在有限时刻爆破, 此外,还导出了解的两个分量同时爆破的必要条件, 并得到了该问题解的一致爆破模式.     

一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

在齐次Dirichlet边界条件研究如下抛物系统其中x_0(t):R⁺→(0,a)是Holder连续函数;常数0≤α,β<1,p_1,p_2,q_1,q_2,k_1,k_2>0.利用正则化方法,在一定的假设条件下证明了经典解的存在性.接着利用比较原理证明了该系统正解的整体存在性和爆破性.最后给出了爆破解的精确爆破速率和爆破模式.     

拟线性退化抛物型方程组解的整体存在性和爆破

该文研究光滑有界区域Ω( R^N (N≥ 1) 上具有齐次Dirichlet边界条件的拟线性退化抛物型方程组 u_t-div(|▽u|^p-2 ▽u) =av^α, v_t-div(|▽v|^q-2 ▽v) =bu^β 的非负解的性质, 其中p, q>2, α, β ≥ 1, a, b> 0是常数. 该文指出上述方程组的解是否在有限时刻爆破依赖于初值、系数 a 与 b以及 αβ 和 (p-1)(q-1)之间的关系.     

一类带有非局部源的退化反应扩散方程组解的整体存在与爆破

研究了一类具有齐次Dirichlet边界条件和带有非局部反应项的退化抛物方程组解的性质.用正则化的方法证明了局部解的存在唯一性,用上下解方法,得到了解的全局存在与爆破的充分条件.     

一类含非局部源的非线性退化抛物型方程

The global existence and finite time blow up of the positive solution for a nonlinear degenerate parabolic equation with non-local source are studied.     

Blow-up for degenerate parabolic equations with nonlocal source

This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source in subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.

     

Global existence and blow‐up solution for doubly degenerate parabolic system with nonlocal sources and inner absorptions

This paper deals with the following doubly degenerate parabolic system with null Dirichlet boundary conditions in a smooth bounded domain Ω ? R^N, where m, n ≥ 1, p, q ≥ 2, r₁, r₂, s₁, s₂ ≥ 1, α, β < 0. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time. Copyright © 2013 John Wiley & Sons, Ltd.     

Strong solutions of a class of fully nonlinear degenerate parabolic equations

This paper is concerned with the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources. After establishing the necessary local existence theorems of strong solutions, we investigate the blow‐up and global existence profile. Copyright © 2015 John Wiley & Sons, Ltd.     

Blow-up for doubly degenerate nonlinear parabolic equations

In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly degenerate nonlinear parabolic equations. The project is supported by the Natural Science Foundation of Fujian Province of China (No. Z0511048)     

Blow-up for a degenerate parabolic equation with nonlocal source and nonlocal boundary

In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.     

A complete upper estimate on the localization for the degenerate parabolic equation with nonlinear source

This paper deals with the Cauchy problem for the degenerate parabolic equation with a strongly nonlinear source where N ≥ 1, p > 2, q ≥ p ? 1, and the blow‐up time T < ∞ . It has been shown that the solution u(x,t) is strictly localized for q ≥ p ? 1, provided that the initial function u₀(x) has a compact support by Liang and Zhao. In addition, if q > 2p ? 1, an upper estimate on the localization in terms of the initial support and the blow‐up time T is partially derived by Liang. In this work, by using the De Giorgi‐type iteration technique, we give a complete estimate on the localization for all q ≥ p ? 1. Copyright © 2014 John Wiley & Sons, Ltd.     

Global existence and blow-up for the degenerate and singular nonlinear parabolic system with a nonlocal source

The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained for the degenerate and singular parabolic system