Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

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带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度

本文提出并研究带有线性外力场的双曲平均曲率流，通过凸曲线的支撑函数，导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论，讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度（即局部解存在的最大时间区间）。     

非线性Klein-Gordon系统生命跨度的上界估计

考虑如下非线性Klein-Gordon系统初边值问题解的生命跨度:utt-Δu+α2u+λuv2=0,vtt-Δu+β2v+λu2v=0(x,t)∈Ω×[0,T),这里,Ω是R3中具有光滑边界的有界域,α,β为非零实数,λ<0,T>0.得到了其解的生命跨度的上界估计,且当能量为正时得到了一个新的能量上界.     

The blowup for 2-D quasilinear wave equations with cubic nonlinearity

For 2-D quasilinear wave equations with cubic nonlinearity and small initial data, we not only show that the solutions blow up in finite time but also give a complete asymptotic expansion of the lifespan of classical solutions. Hence we solve a problem posed by S. Alinhac and A. Hoshiga. Moreover, as an application of this result, we prove the blowup of solutions for the nonlinear vibrating membrane equations.     

Effect of polysaccharides extracted from Sipunculus nudus (SNP) on the lifespan and immune damage repair of Drosophila melanogaster exposed to Cd (VI)

The water-soluble polysaccharides extracted from Sipunculus nudus (SNP) was investigated on the lifespan and immune damage repair of Drosophila melanogaster exposed to Cd (VI). SNP increased superoxyde dismutase (SOD), nitrogen monoxide (NO), glutathione peroxidase (GSH-Px) and total anti-oxidation competence (T-AOC), with decreased malondialdehyde (MDA) on D. melanogaster demonstrated that SNP could attenuate oxidative damage of D. melanogaster Exposed to Cd (VI). Real-time PCR and western blot analysis showed that SNP enhanced the gene expression of Diptericin, Drosomycin, Defensin, PGRP-LC and the protein level of Toll, p-JNK and Relish， that suggested the promoting effect of SNP on the immune damage repair of D. melanogaster exposed to Cd (VI). The increased level of Indy, Parkin and AMPK indicated the regulated effect of SNP on the longevity-related pathways through ageing-related moleculars of D. melanogaster exposed to Cd (VI). These results suggested that SNP could also improve the lifespan of D. melanogaster exposed to Cd (VI).     

The blowup mechanism for 3-D quasilinear wave equations with small data

For a class of special three-dimensional quasilinear wave equations, we study the blowup mechanism of classical solutions. More precisely, under the nondegenerate conditions, any radially symmetric solution with small initial data is shown to develop singularities in the second order derivatives while the first order derivatives and itself remain continuous, moreover the blowup of solution is of “cusp type”.