共查询到20条相似文献,搜索用时 10 毫秒
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SEMIDISCRETIZATION IN SPACE OF NONLINEAR DEGENERATE MRABOLIC EQUATIONS WITH BLOW-UP OF THE SOLUTIONS
Tetsuya Ishiwata 《计算数学(英文版)》2000,(6)
1. IntroductionLet n be a bounded domain in AN with smooth boundary Off. We consider thefollowing initial boundary value problem:where 6, p are positive constants and "o(x) is a nonnegative bounded continuous function on fi.When N = 1 and 5 ~ 2, the problem arises in a model for the resistive diffusion of aforce--free magnetic field in a plasma confined between two walls in one dimension (see[5], [8], [9], [10] and [14]). Equation (1) also describes the evolution of the curvatureof a locally… 相似文献
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This article is concerned with the position of blow-up points, blow up rate and an isoperimetric problem for the equation u_t = Δu^m + u^p(p > m ≥ 1) in a convex bounded domain. 相似文献
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考虑了有界区域上一类非线性退化波动方程的初边值问题.通过改进Vitillaro,Li和Tsai的方法,建立了非正的初始能量以及正的初始能量下解的爆破结果.同时,还给出了解的生命跨度估计. 相似文献
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In this paper we give a detailed discussion about the effect of quantitative relation between p and m on the properties of the solutions to nonlinear parabolic equation u_t - (u^mu_x)_x = u^p. 相似文献
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研究了一类具有非线性边界条件的拟线性方程组解的整体存在性和爆破.通过构造不同类型的上、下解并利用M-矩阵的基本性质,给出了非负解整体存在性的充要条件.借助这些新结果,给出了Fuiita型临界曲线,把最近的结果推广到了更一般的方程. 相似文献
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一类半线性积分微分方程初边值问题的爆破解和全局解 总被引:2,自引:0,他引:2
本文研究初边值问题的爆破解和全局解,证明了在f的凸性假设和一定的增长性假定下解在有限时刻爆破,而在f的其他假设下证明了全局解的存在性。 相似文献
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陈明玉 《数学的实践与认识》2008,38(24)
研究了RN中一般区域上的一族带非线性梯度项的双重退缩抛物方程解的Blow-up性质.通过构造适当的辅助函数,利用特征函数法和不等式技巧,给出了其齐次Dirichlet边值问题的正解产生Blow-up的充分条件:利用能量方法,证明了其Cauchy问题非平凡整体解的不存在性.方法也适用于研究其它带非线性源的退缩非线性抛物方程解的Blow-up问题. 相似文献
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该文构造了三维磁流体方程组的若干分离变量型和自相似型显式爆破解. 相似文献
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Wen Jun SUN Shu WANG 《数学学报(英文版)》2005,21(4):847-854
In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive (weak) solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition. 相似文献
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本文考虑具有 Neumann边界条件 u/n=ev, v/η=eu在 SR ×(0,T)热方程组。ut=△u,vt=△v在BR×(0,T)解的爆破性质·我们给出了爆破速度估计并证明了爆破仅在边界上发生. 相似文献
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具有非局部源的退化半线性抛物型方程组解的爆破 总被引:4,自引:0,他引:4
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 . 相似文献
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YE Yao-jun LIU Qiu-xiang 《数学季刊》2005,20(4):390-394
In this paper we study the decay estimate of global solutions to the initialboundary value problem for double degenerate nonlinear parabolic equation by using a difference inequality. 相似文献
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ZHENG Tingting ZHAO Junning 《偏微分方程(英文版)》2009,(3):199-204
In this note we study the nonexistence of nontrivial global solutions on S = R^N × (0,∞) for the following inequalities:|u|t≥△(|u|^m-1u)+|u|^q and |u|t≥div(|△u|^p-2△|u|)+|u|^q.When m,p,q satisfy some given conditions, the nonexistence of nontrivial global solution is proved, without taking their traces on the hyperplans t = 0 into account. 相似文献
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Espen R. JakobsenKenneth H. Karlsen 《Journal of Differential Equations》2002,183(2):497-525
Using the maximum principle for semicontinuous functions (Differential Integral Equations3 (1990), 1001-1014; Bull. Amer. Math. Soc. (N.S)27 (1992), 1-67), we establish a general “continuous dependence on the non- linearities” estimate for viscosity solutions of fully nonlinear degenerate parabolic equations with time- and space-dependent nonlinearities. Our result generalizes a result by Souganidis (J. Differential Equations56 (1985), 345-390) for first- order Hamilton-Jacobi equations and a recent result by Cockburn et al. (J. Differential Equations170 (2001), 180-187) for a class of degenerate parabolic second-order equations. We apply this result to a rather general class of equations and obtain: (i) Explicit continuous dependence estimates. (ii) L∞ and Hölder regularity estimates. (iii) A rate of convergence for the vanishing viscosity method. Finally, we illustrate results (i)-(iii) on the Hamilton-Jacobi- Bellman partial differential equation associated with optimal control of a degenerate diffusion process over a finite horizon. For this equation such results are usually derived via probabilistic arguments, which we avoid entirely here. 相似文献
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本文指出了文[1]所给条件的自身矛盾性以及运用凸性方法处理拟线性抛物型方程Blow-up性质的缺陷,同时提出了处理这类问题的较恰当的方法. 相似文献