共查询到19条相似文献,搜索用时 81 毫秒
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研究了具有依赖于时间的系数的非线性抛物方程解的爆破现象.对已知数据项进行一定的假设并设置一些辅助函数,应用微分不等式技术,得到了方程的解发生爆破的条件.当爆破发生时,分别推导了方程在二维区域和三维区域上解的爆破时间的下界. 相似文献
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研究非线性Klein-Gordon方程的初边值问题,运用位势井方法,在E(0)d的情况得到了方程解的整体存在和爆破.在临界能量状态得到了整体解的存在性与不存在性.最后使用凸性方法,得到某些具有高初始能量解的爆破. 相似文献
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姜玲玉 《纯粹数学与应用数学》2013,(5):458-464
研究广义可压缩弹性杆方程解的爆破条件及尖峰孤立波解的存在性.首先利用所建立的爆破准则,给出一个方程在有限时刻爆破的充分条件.其次,严格证明了其尖峰孤立波解的整体存在性.该结果丰富了此类Camassa-Holm型方程的研究. 相似文献
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《数学物理学报(A辑)》2018,(5)
该文考虑了三维空间中具有非局部源的p-Laplace方程分别在Dirichlet边界条件和Robin边界条件下解的爆破性质,通过构造辅助函数并利用微分不等式的技巧,得到了两种边界条件下方程解的爆破时间下界估计.另外,给出了方程解在L~2-范数下不会发生爆破的充分条件· 相似文献
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应用Hasimoto变换,给出了双曲空间H~2上的Landau-Lifshitz-Gilbert(LLG)方程的一等价系统.基于该等价模型,证明了在小初值条件下LLG方程解的全局存在性.到目前为止,还未见到有文章在双曲空间下给出带阻尼项方程的精确解.基于导出的等价方程,首次构造了一显式小初值的整体解.另外,也给出了等价系统的自相似有限时间爆破解.在作者发表的论文[25]中,构造了在H~2上没有吉尔伯特阻尼项方程的有限时间爆破解.带阻尼项的LLG方程的有限能量解能否在H~2上演化出有限时间爆破或全局光滑这一问题尚不清楚.该文给出的自相似有限时间爆破解是在整个空间区域上的有限能量解.该例子给出了这个问题的一个回答. 相似文献
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强阻尼非线性Klein—Gordon方程解爆破的充要条件 总被引:1,自引:0,他引:1
考虑一类具强阻尼非线性Klein-Gordon方程解的性态.先用修正能量法讨论了整体解的存在性,然后用改进和简化的凸性方法,利用势阱理论和能量函数得到了该方程在动力学边界条件下解爆破的充要条件. 相似文献
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In this paper, an explicit lower bound for the blow-up time is obtained to a parabolic–parabolic Keller–Segel system, the blow-up conditions of which were established with an upper bound of blow-up time by Cie?lak and Stinner [T. Cie?lak, C. Stinner, Finite-time blowup and global-in-time unbounded solutions to a parabolic–parabolic quasilinear Keller–Segel system in higher dimensions, J. Differential Equations 252 (2012) 5832–5851]. 相似文献
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L.E. Payne 《Applicable analysis》2013,92(6):699-707
By means of a first-order differential inequality technique, sufficient conditions are determined which imply that blow-up of the solution does occur or does not occur for the semilinear heat equation under Robin boundary conditions. In addition, a lower bound on blow-up time is obtained when blow-up does occur. 相似文献
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L.E. Payne 《Journal of Mathematical Analysis and Applications》2007,328(2):1196-1205
We consider an initial-boundary value problem for the semilinear heat equation whose solution may blow up in finite time. We use a differential inequality technique to determine a lower bound on blow-up time if blow-up occurs. A second method based on a comparison principle is also presented. 相似文献
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In this article, we study the blow-up phenomena of generalized double dispersion equations u_(tt)-u_(xx)-u_(xxt) + u_(xxxx)-u_(xxtt)= f(u_x)_x.Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T~* depending on sign and size of initial energy E(0). Furthermore, a lower bound for blow-up time T~* is determined by means of a differential inequality argument when blow-up occurs. 相似文献
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The initial boundary-value problem for the equation of ion-sound waves in a plasma is studied. A theorem on the nonextendable solution is proved. Sufficient conditions for the blow-up of the solution in finite time and the upper bound for the blow-up time are obtained using the method of test functions. 相似文献
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L. E. Payne 《Applicable analysis》2013,92(10):1301-1311
We consider an initial boundary value problem for the semilinear heat equation under homogeneous Neumann boundary conditions in which the solution may blow up in finite time. A lower bound for the blow-up time is determined by means of a differential inequality argument when blow up occurs. Under alternative conditions on the nonlinearity, some additional bounds for blow-up time are also determined. 相似文献
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This paper studies the blow-up property of weak solutions to an initial and boundary value problem for a nonlinear viscoelastic hyperbolic equation with nonlinear sources. A lower bound for the blow-up time is given. 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