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KONG Dexing 《数学年刊A辑(中文版)》2000,21(4):413-440
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow” decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data. 相似文献
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In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two space variables, we give a lower bound of the life-span of classical solutions to the hyperbolic geometric flow with asymptotic flat initial Riemann surfaces. 相似文献
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LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA 总被引:7,自引:0,他引:7
KONG Dexing 《数学年刊B辑(英文版)》2000,21(4):413-440
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow“ decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the casethat the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data. 相似文献
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In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2]. 相似文献
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李明融 《数学物理学报(B辑英文版)》2010,(4):1227-1234
In this article, we study the following initial value problem for the nonlinear equation
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
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In this article, we study the following initial value problem for the nonlinear equation 相似文献
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KONG DEXING 《数学年刊B辑(英文版)》2000,(4)
1. IntroductionConsider the following quasilinear systeman on~ A(u)~ = 0, (1.1)ot oxwhere u ~ (ul,' t u.)" is the unknown vector function of (t, x) and A(u) ~ (ail(u)) is ann x n matrix with suitably smooth elements ail(u) (i, j = 1,... ) n).Suppose that the system (1.1) is strictly hyperbolic in a neighbourhood of u = 0, namely,for any given u in this domain, A(u) has n distinct real eigenvalues Al(u), AZ(u),' j A.(u)such thatAl(u) < AZ(u) <' < A.(u). (1.2)For i = 1,',nl let h(u… 相似文献
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