R^(1+3)中球形非线性脉冲波的存在性分析  

Analysis on Existence of Spherical Nonlinear Pulses in R^(1+3)

作　　者：袁明生[1] 王学峰[2] 唐红兵[2] 

机构地区：[1]上海交通大学应用数学系,上海200240 [2]石河子大学师范学院数学系,新疆石河子832003

出　　处：《石河子大学学报（自然科学版）》2004年第4期360-363,共4页Journal of Shihezi University(Natural Science)

基　　金：中国自然科学基金(1013050)

摘　　要：讨论了非线性脉波动方程Λuε+F(|tuε|p-1tuε)=0,(t,x)∈[0,∞]×R3uεt=0　=εJ+1U0(r,r-r0ε),tuεt=0　=εJU1(r,r-r0ε)在1<p<∞的条件下所描述的球形脉冲波的局部和全局存在性问题,并对次临界(1<p≤2)和超临界(2<p≤∞)的情形都进行了讨论,为进行解的渐进分析做了必要的准备。We discuss local and giobal existence of spherical nonlinear pulses of wave equationΛu~ε+F(|_tu~ε|^(p-1)_tu~ε)=0(t,x)∈×R^3 u~ε_(t=0)=ε^(J+1)U_0(r,r-r_0ε),_tu~ε_(t=0)=ε^(J)U_1(r,r-r_0ε)with 1<p<∞ and F being uniformly Lipschitzean on R.Our discussion is in both subcritical case when 1<p≤2 and supercritical case when 2<p≤∞,which is prepared to make asymptotic analysis of solutions to the system mentioned above.

关 键 词：一致lip 非线性 球形对称 脉冲 紧支集 

分 类 号：O175.27[理学—数学]