数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (1): 16-22.
杨晗, 刘法贵
YANG Han, LIU Fa-Gui
摘要:
The authors consider the Cauchy problem for the following nonlinear wave equations
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utt − u = |∇v|2,
vtt − v = (u)2,
u(0, x) = "u0(x), ut(0, x) = "u1(x),
v(0, x) = "v0(x), vt(0, x) = "v1(x),
where x ∈ R3, t ≥ 0, " > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ", then the lifespan T(") satisfies the folowing inequalities C1 ≤ lim"!0 " ln T(") ≤ C2.
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