带诺伊曼边界条件的小初值耗散半线性波动方程外问题解的破裂及生命跨度估计

Blow up for Small Initial Data Dissipation Semilinear Wave Equation Exterior Problem Solution with Neumann Boundary Condition and Life Span Estimation

运用试探函数研究了外区域上带诺伊曼边界条件的小初值耗散波动方程,证明:当非线性指数p满足1<p≤1+2/N(N为空间维数)时解将在有限时内破裂;当1<p<1+2/N时,得到了解的生命跨度上界估计。

Small initial d ata d is s ip a tio n wave eq u at io n wi th Neuman n b o u n d a ry co n dition in e x te r io r domain was studied by using test funct ion method？ proving that the solut ion will blow up2the power p of th e n o n l in e a r te rm sa t is f ie s 1〈I p^1 ＋ ^（N re fe rs to th e n umb e r of 2Meanwhi le,we have got the upper bound of the l ifespan for 1 〈p〈1 ＋ n .