关于半线性热方程的死角性质

本文考虑下述问题：这里，．本文证明了在发生死角时只有有限个死角点．     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

某些非线性波动方程的解的爆破

本文探讨某些非线性波动方程于混合问题解的爆破性于高阶方程情形,籍引入一类“爆破因子Ｋ（ｕ,ｕｔ）”而得到某些新的结果,它扩充了（４）中对不同的非线性条件和初值条件的常见情形,主要结果是定理１与定理６。     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

非线性拟抛物型积分微分方程的初边值问题和初值问题

本文研究非线性拟抛物积分微分方程的初边值问题和初值问题。运用Galerkin方程结合能量估计证明了问题的整体强解的生存性、唯一性和稳定性，最后在一定条件下讨论了初边值问题整体解的不存在性和爆破问题。     

BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

gi. IntroductionThis paper deals with solutionS of certain nonlinear wave equationS Of the formcorresponding to Antial conditionSwuersis the wave OPerstor.we are interested in showing the ~ up" Of solutions to (1.1)--(1.2). For that, wereIf ac ~ 1)(n ~ 1) > 2, global solutions of ~ equation subject to very general perturbationsof order p exist Provided the initial data are swhciently small (see I6] and references therein).We are also interested in esthaattw the take when "blow up" occurs. …     

带有非线性边界条件强耦合半线性抛物方程组解的Blowup性态

讨论了一类非线性边界条件强耦合半线性抛物方程组解的Ｂｌｏｗｕｐ性态     

Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model

In this paper, a delayed Holling-Tanner predator-prey model with ratio-dependent functional response is considered. It is proved that the model system is permanent under certain conditions. The local asymptotic stability and the Hopf-bifurcation results are discussed. Qualitative behaviour of the singularity (0,0) is explored by using a blow up transformation. Global asymptotic stability analysis of the positive equilibrium is carried out. Numerical simulations are presented for the support of our analytical findings.     

Blow up of critical semilinear wave equations on Schwarzschild spacetime

In this paper, we established the blow up theorem for critical semilinear wave equations with focusing nonlinear term on Schwarzschild spacetime. Concavity method is used to prove the main result, which was introduced by Levine–Payne in the papers Levine and Payne (1974)  and  and Levine (1973) [7] in 1970s. Also, a new auxiliary function with parameter β$\beta$ is constructed following the idea from Payne (1975) [13], in order to guarantee that the result holds without any assumption on the initial data and initial energy.     

一类耗散型Degasperis—Procesi方程解的blow—up

研究了带耗散项A（虬一％）的Degasperis—Procesi方程的初值问题，由Kato定理得到初值问题的解的局部适定性结果，然后研究了解的blow-up现象．