共查询到20条相似文献,搜索用时 78 毫秒
1.
讨论一类基本的半线性抛物型方程,其在物理上对应具有内部热源的热传导问题,提出了一些爆破的充分条件,讨论了有限爆破点与径向对称情况下的爆破点,并证明爆破速率之上界与下界. 相似文献
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该文讨论了一类带梯度依赖势和源的粘性Cahn-Hilliard方程解的爆破现象.使用能量方法,微分不等式和积的导数公式建立了爆破准则和确定了爆破时间的上界;利用微分不等式和积的导数公式确定了爆破时间的下界. 相似文献
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本文讨论具齐次Dirichlet边界条件非局部源反应扩散方程组的爆破解,给出四类同时爆破与不同时爆破现象的判定指标,这四类爆破现象包含:(i)存在不同时爆破;(ii)同时爆破与不同时爆破共存;(iii)任意爆破必是同时爆破;(iv)任意爆破必是不同时爆破. 相似文献
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讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论. 相似文献
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本文讨论了一个带有梯度的非线性波动方程解的爆破性质,证明了解在有限时间内爆破,推广了文[1]的结果. 相似文献
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带调和势的非线性Schrdinger方程爆破解的L~2集中率 总被引:1,自引:0,他引:1
本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率. 相似文献
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本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率. 相似文献
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讨论了2维Zakharov方程组的Caucgy问题的爆破解.对径向对称爆破解,证明了原点0是爆破点,并建立了当t→T(爆破时间)时,集中率的下界. 相似文献
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This paper deals with asymptotic behavior of solutions to a heat system with absorptions and coupling positive multi-nonlinearities. It is known that although absorption mechanisms may affect such as blow-up criteria, blow-up time, and initial data required for blow-up solutions, they cannot change blow-up rates of solutions in general. It has been reported in the current literature that blow-up rates for scalar equations with absorptions are all absorption-independent. In a previous paper of the authors, four absorption-independent simultaneous blow-up rates were obtained already for the same problem under weak absorptions. The present paper will furthermore prove that if the absorptions are unbalanced in the model (i.e., the absorption is stronger for one component and weaker for another), then there are in addition eight possible absorption-related blow-up rates for the model, besides the four absorption-independent ones. This exposes a significant difference between scalar and coupled nonlinear parabolic equations with absorptions. 相似文献
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L. F. Chacón-Cortés Andrés Vargas 《P-Adic Numbers, Ultrametric Analysis, and Applications》2017,9(3):183-196
The problem of existence of solutions to p-adic semilinear heat equations with particular nonlinear terms has already been studied in the literature but the occurrence of blow-up phenomena has not been considered yet. We initiate the study of finite time blow-up for solutions of this kind of p-adic semilinear equations, proving that this phenomenon always arises under appropriate assumptions in the case when the exponent of nonlinearity times the dimension is strictly less than the order of the operator. 相似文献
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L.E. Payne 《Journal of Mathematical Analysis and Applications》2007,335(1):371-376
In this paper we consider two different initial-boundary value problems in temperature dependent viscous flow when the temperature equation has a nonlinear heat source term. When blow-up occurs we derive lower bounds for the blow-up time in each case. 相似文献
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This paper considers a heat system with localized sources and local couplings subject to null Dirichlet boundary conditions,
for which both total and single point blow-up are possible. The aim of the paper is to identify the total and single point
blow-up via a complete classification for all the nonlinear parameters in the model. As preliminaries of the paper, simultaneous
versus non-simultaneous blow-up of solutions is involved, too. The results are then compared with those for another kind of
heat system coupled via localized sources in a previous paper of the authors. 相似文献
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Fei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2189-2198
This paper deals with the blow-up for a system of semilinear r-Laplace heat equations with nonlinear boundary flux. It is shown that, under certain conditions on the nonlinearities and data, blow-up will occur at some finite time, and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
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Cristian Enache 《Applied Mathematics Letters》2011,24(3):288-292
This note deals with a class of heat emission processes in a medium with a non-negative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, we make use of a first-order differential inequality technique to establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addition, the same technique is used to determine a lower bound for the blow-up time when blow-up occurs. 相似文献
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Juliá n Ferná ndez Bonder Julio D. Rossi 《Proceedings of the American Mathematical Society》2001,129(1):139-144
In this paper, we study the blow-up problem for positive solutions of a semidiscretization in space of the heat equation in one space dimension with a nonlinear flux boundary condition and a nonlinear absorption term in the equation. We obtain that, for a certain range of parameters, the continuous problem has blow-up solutions but the semidiscretization does not and the reason for this is that a spurious attractive steady solution appears.
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We study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, we obtain the existence of global solution and blow-up at +∞ under some suitable conditions. On the other hand, the results for decay estimates of the global solutions are also given. Our result in this paper means that the polynomial nonlinearity is a critical condition of blow-up in finite time for the solutions of semilinear heat equations. 相似文献