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61.
This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space Hup>1up>(Ω) × L2(?Ω) with boundary data in L2 due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from Hup>1up>(Ω) into L2(Ω), or L2(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy. 相似文献
62.
A. Pulkkinen 《Mathematical Methods in the Applied Sciences》2011,34(16):2011-2030
We consider the blow‐up of solutions for a semilinear reaction‐diffusion equation with exponential reaction term. It is known that certain solutions that can be continued beyond the blow‐up time possess a non‐constant self‐similar blow‐up profile. Our aim is to find the final time blow‐up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach works also for the power nonlinearity. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
63.
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr(o)dinger equations.The local and global well-posedness are proved with values in the space ∑(Rn) ={f ∈ H1(Rn),| · |f ∈ L2(Rn)}.When the nonlinearity is focusing and L2-supercritical,the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential.Especially for the repulsive case,the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time.Thus,compared with the deterministic equation for the repulsive case,the blow-up condition is stronger on average,and depends on the regularity of the noise.If φ =0,our results coincide with the ones for the deterministic equation. 相似文献
64.
65.
Hon Hung Terence Liu 《Mathematical Methods in the Applied Sciences》2019,42(16):5383-5389
The diffusion problem in a subdiffusive medium is formulated by using the fractional differential operator. In this paper, we consider a fractional differential equation with concentrated source. The existence of the solution in a finite time is given. The finite time blow‐up criteria for the solution of the problem is established, and the location of the blow‐up point is investigated. 相似文献
66.
In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions gi(i = 1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature. 相似文献
67.
This paper concentrates on considering the down/up crossing property of weighted Markov collision processes. The joint probability generating function of down crossing and up crossing numbers of weighted Markov collision processes until its extinction are obtained by constructing and studying a related multi-dimensional Markov chain. Hence, the joint probability distribution of down crossing and up crossing numbers and the mean numbers are obtained. 相似文献
68.
阎格 《新疆大学学报(理工版)》1993,10(4):34-41
对Fujita类方程组解的整体存在性和如何在有限时间内发生Blow up现象的研究,具有实际意义.M.Escobedo等人对其二元情形曾做过研究,即在[1]中对非线性项单一如v~(?)或u~(?)的Cauchy问题进行了讨论,本文意在上述基础上作些推广:修改非线性项如u~(?)v~(?)或u~qv~n情形,利用上、下解的方法,证明了在一定条件下,推广后的Cauchy问题亦有[1]中指出的类似的结果. 相似文献
69.
多重休假的带启动期Geom/G/1排队 总被引:10,自引:2,他引:8
本文研究多重休假的带启动期的Geom/G/1离散时间排队。给出稳态队长,等待时间分布的母函数及其随机分解结果,推导出忙期,假期和启动期的母函数等。 相似文献
70.
Er3+:Yb3+共掺杂氟氧混合物玻璃的上转换发光研究 总被引:3,自引:1,他引:2
制备了化学配方为 (5 0 -x)GeO2 ·PbF2 ·WO3·(6 +x)CdF2 ·1 4Yb2 O3·0 6Er2 O3(x =10 ,2 0 ,30 )氟氧混合物玻璃。研究了 930nm发光二极管激发下Er3+ :Yb3+ 共掺杂情形下的Er3+ 离子的上转换发光特性 ,观测到了Er3+ 离子中心波长位于 5 4 3,5 5 0和 6 5 5nm处的三个强荧光发射带。通过对样品的反斯托克斯喇曼光谱的测量 ,确定了基质的最大声子能量 ,在此基础上分析了上转换荧光的产生机制。利用基质的平均电负性差和平均阳离子场强这两个参数 ,讨论了基质材料中GeO2 和CdF2 含量的调整对上转换发光的影响。 相似文献