R^(1+3)中球形非线性脉冲的聚焦分析

Caustic Analysis of Sphercial Nonlinear Pulses in R^(1+3)

讨论了非线性波动方程(2 t-Δx)uε+F( |tuε| P -1 tuε) =0 ,(t,x)∈ ( 0 ,∞ )×R3,uε| t=0 =εU0 =εU0 r,r-r0ε ,tuε| t=0 =U1 r,r-r0ε在次临界情形下 (即 1 <p <2时 )所描述的球形脉冲波的解的误差分析 ,其中在F上是一致Lipschitiz的。在小初值情形下讨论了主轮廓(leadingprofiles)

In this paper,we discuss the asymptotic behavior of spherical nonlinear pulses of wave equation (~2_t-△_x)u~ε+F(|_tu~ε|^(P-1)_tu~ε)=0,(t,x)∈(0,∞)×R^3,u~ε|_(t=0)=εU_0=εU_0r,r-r_0ε,_tu~ε|_(t=0)=U_1r,r-r_0εwith being uniformly Lipschitiz on R.In the subscritic case, 1<p<2,we discuss the local existence of leading profiles,asymptotic behavior of solutions and its error analysis near the focus, under the condition of small initial data.