18

()⎰⎰⎰⎰+⎪⎪⎭⎫ ⎝⎛-=

+-≤-1031022103102214

1dx u C dx u p p dx u C dx u u p p p x p p x p

再由(4.14)得到 ()εε4101012

121C dx u p dx u p p I p x p ++⎪⎪⎭⎫ ⎝⎛-≤⎰⎰+ 像估计2I 那样再估计3I

()⎰⋅-≤-1

0131dx u v u p p I x x p ()()()()⎰⎰⎰⎰⎰⎰⎰⎰++--++⎪⎪⎭⎫ ⎝⎛-=⋅+⎪⎪⎭⎫ ⎝⎛-=+-≤⎪⎪⎭

⎫ ⎝⎛⋅⎪⎪⎭⎫ ⎝⎛-≤10101261012210

102522102510221

021211411dx

v C dx u p dx u p p dx v u C dx u p p dx v u C dx u u p p dx v u u u p p p x p x p

x p x p x p x p x p x p εε 由此并结合(4.11)得

()εε7101102231C dx u p dx u p p I p x p ++⎪⎪⎭⎫ ⎝⎛-≤⎰⎰+ (4.16)

另外注意到：

()⎰⎰+≤+1

08101εεC dx u p dx u p p (4.17)

综合(4.13-4.17)得 ()()⎰⎰⎰⎰⎰++-⎪⎪⎭⎫ ⎝⎛--≤+++1011011012

2101014εεC dx u p dx u p dx u p p dx u dx u dt d p p x

p p p ⎰⎪⎪⎭⎫ ⎝⎛-+10221dx u p p x p +()εε4101C dx u p p +⎰+