Nghiem lai dinh ly Stokes.. Tim phAn b6 nhiet trong thanh.
Trang 1e0 cno DUc vA DAo TAo
.a DAI HOC HUE
Ho vd, ten thi sinh:
56 b6o danh:
srNH sAU D4r HOC NAM 2OO7 thi: To5.n cho Vat li
(dd,nh cho Cao hqc) g'ian ld,m bd,i,: 180 phrit
KY THI TUYEN)
M6n
Thdi
C A U I
1 XAc dinh c6c he s6 Lame trong hO toa d6 tru (p,g, r) Tri d6,
d i v A ' t r o n g h O to a d 6 t r u ( p , g , r )
2 Tinh luu s6 cria hb,m vecto: F - @ili + (br)i @,b 1d, hX,ng sd) doc theo dulng trbn b6,n kinh ft nXm trong mit phH,ng rOa, c6 tAm trtng vdi g6c toa d6 Nghiem lai dinh ly Stokes.
, \ 1 J , t t )
trm bleu tnuc cua
CAu II GiAi Uai toan ' I
t
r 1 l , t > 0 ,
t ) 0 ,
) r
s i n 1 z 0 < r < (
(
CAu III Mot thanh dbng chd,t, d6,t doc theo truc Or, c6 do ddi (., m1t chung quanh c6,ch
ban dhu cria thanh ducvc cho bdi
u ( r , o ) : t " ( n a ; " 1 , o ( n 1 ( ( c I d h i n g s d )
Tim phAn b6 nhiet trong thanh
CAu IV Tim hbm u(r,y) dibu ho), trong hinh trbn 12 + y2 < 1 vd, thoA man dibu ki6n tren bien 12 + A2 : 1 cria hinh trbn (cho trong toa d6 cqc)
" l _ sin2e, ( 0 S p S 2 r )
l r : 1 CAu V Chfng minh rXng hh,m
u(r,a,z,t): t I Lkr(r,a,z)6il+ Ak r(r,a,z)ffi),
k : O L
thoA m6,n phucrng trinh truybn s6ng
' t l t t : 1 1 r , * uaa *'ltrzz, (rrArz, t) e Ra
( r , , a , z ) e R 3
u ( 0 , t )
-a2rtrr*, o (
u ( ! , t ) : 0 ,
u ( r , 0 ) - 0 , u t ( r , 0 ) :
vh, c5,c dibu kien ban dhu
I u ( r , g , 2 , 0 ) - r ( r , U , , z ) ,
1 r , ( r , a , 2 , 0 ) - u ( r , a , z ) ,
Ap dung, gidi bbi to6n
(
" "
\ u ( " , U , 2 , 0 ) - 1 2 - A 2 + 2 r ' ,
L r r ( r , a , 2 , 0 ) - a 3 * z z l r z l r
Ghi chir: Cdn bo coi, thi, kh6ng gi,d,i thi'ch gi th€m
* 1 , ( r , a , z ) e I R 3