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151.
Ezequiel R. Barbosa Marcos Montenegro 《Bulletin of the Brazilian Mathematical Society》2008,39(3):427-445
In this work we present some properties satisfied by the second L
2-Riemannian Sobolev best constant along the Ricci flow on compact manifolds of dimensions n ≥ 4. We prove that, along the Ricci flow g(t), the second best constant B
0(2, g(t)) depends continuously on t and blows-up in finite time. In certain cases, the speed of the explosion is, at least, the same one of the curvature operator.
We also show that, on manifolds with positive curvature operator or pointwise 1/4-pinched curvature, one of the situations
holds: B
0(2, g(t)) converges to an explicit constant or extremal functions there exists for t large.
相似文献
152.
Ma Renyi 《数学学报(英文版)》1996,12(4):379-384
In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.Supported in part by the NSF of P. R. China and the Foundation of Chinese Educational Committee for Returned Scholars. 相似文献
153.
本文研究一类带双势的具有临界幂的非线性Schrodinger方程的初值问题.得到该方程爆破解的L2集中性质并在此基础上得到其爆破解为径向对称情形的L2集中速率. 相似文献
154.
本文讨论在在非线性边界条件下反应-扩散方程解的爆破.当非线性项f,g满足一定的条件时,我们得到其解在有限时间内爆破. 相似文献
155.
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
156.
We consider one system of nonlinear Schrödinger equations and find the conditions when its solution blows up. 相似文献
157.
Satyanad Kichenassamy 《Journal of Functional Analysis》2005,222(1):98-113
Let Ω⊂Rn be a bounded domain of class C2+α, 0<α<1. We show that if n?3 and uΩ is the maximal solution of equation Δu=n(n-2)u(n+2)/(n-2) in Ω, then the hyperbolic radius is of class C2+α up to the boundary. The argument rests on a reduction to a nonlinear Fuchsian elliptic PDE. 相似文献
158.
Viorel Barbu Irena Lasiecka Mohammad A. Rammaha 《Transactions of the American Mathematical Society》2005,357(7):2571-2611
In this article we focus on the global well-posedness of the differential equation , where is a sub-differential of a continuous convex function . Under some conditions on and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assumptions on the parameters we establish the existence of global generalized solutions. With further restrictions on the parameters we prove the existence and uniqueness of a global weak solution. In addition, we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent is greater than the critical value , and the initial energy is negative. We also address the issue of propagation of regularity. Specifically, under some restriction on the parameters, we prove that solutions that correspond to any regular initial data such that , are indeed strong solutions.
159.
Suppose π: X → Y is a smooth blow-up along a submanifold Z of Y between complex Fano manifolds X and Y of pseudo-indices iX and iY respectively (recall that iX is defined by iX :=min {−KX·C | C is a rational curve of X}). We prove that
if 2 dim (Z) < dim (Y)+iY −1 and show that this result is optimal by classifying the ‘boundary’ cases. As expected, these results are obtained by studying rational curves on X and Y. 相似文献
160.
In this paper we consider the Cauchy problem for the hyperbolic system
with null boundary conditions and we prove a local (in time) existence and uniqueness theorem inC
b
0, 1
and, for a special class of initial data, a blow-up result.Dedicated to Constantine Dafermos on his 60th birthdayThis research was supported by FCT and FEDER. 相似文献
0,t \geqslant 0} \\ {u_t + \tfrac{1}{2}(a^2 + u^2 )_x = 0} \\ \end{array} } \right.$$ " align="middle" vspace="20%" border="0"> |