[分析] PDE
3
1. Let u be a solution of the wave equation in all of R X R.
suppose a > 0 and u(x,0) = u (x,0) = 0 for |x|>a.
t
Show that there is C > 0 s.t.
2
∫ u (x,t) dx ≦ C , for all t≧0.
R^3
(Hint : show that there is a finite energy solution of
w - △w = 0 s.t. w = u. )
t t
2. 已解決
=========================================================================
第一題我看提示的地方， 就先假設 e(t) = (1/2)∫(w_t)^2 + |▽w|^2 dx
然後就不知道怎麼做下去了...T.T
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 115.43.192.87
※ 編輯: smartlwj 來自: 140.116.90.149 (02/27 17:38)
推
02/28 09:03, , 1F
02/28 09:03, 1F
→
02/28 09:04, , 2F
02/28 09:04, 2F
→
02/28 09:05, , 3F
02/28 09:05, 3F
→
02/28 09:07, , 4F
02/28 09:07, 4F
→
02/28 09:10, , 5F
02/28 09:10, 5F
討論串 (同標題文章)