, u (x, t)= X (x) T (t).
-
:
,
194. b, . , -
u (r,t) t >0.
.
, u (r,t) =R (r) T (t) -
,
195. b, t ³0 - q, . .
. :
- , ,
v (r,t)
194. :
196.
. , w=t (x+ 1)
u (x,t) =v (x,t) + t (x+ 1) v (x,t)
- :
,
. :
k= 2 m , , , - :
197. b u 0. , u 1 >u 0. t >0.
198. l - , u (x, 0) =l-x, x= 0 , x=l .
199. l, . x=l - , x= 0 , u (0 ,t) =At, A . u (x,t) t >0.
|
|
201.
202.
203.
204.
205.
206.
224.
225.
7.
2-
(65)
v - . - ,
, (65) -
(66)
- , -
v=n, n= 0,1,2,, Jn (x) J-n (x) , (67),(68). - - -:
Nn (x) Jn (x), -
, - - = 0. (66) v=n - (65)
(70)
-
(71) v= 0
(72)
(72)
(73)
J 0(x), J 1(x), , Jn (x), , . Jn (x)=0 - :
, , Jn (x) - . - J 0(x):
, k () =0, ( (61 62)):
(74)
(65) :
(75)
, - , k (x) =x, k (0)=0.
- :
k (r) =r p (r) =r. , x=λr, x .
(76)
(70), r (76)
(78)
(77) (79) , Jn (0)=0, Nn (0)=∞, (77)
, 2=0. 1=1, -
(78)
(79)
r [0, l ], ..
(79):
(80)
|
|
(. (42))
(81)
(82) -
(78), 2=0 1=1,
(82 83)
r [0, l ],
229. - l, , - ,
.
,
R (l)=0, :
(.(35))
r, :
T (t)
k,
(81) (. (73))
,
J 0(x)=0.
230 l, , ,
.
, u (r,t) =R (r) T (t). -
, ,
h
,
231. , - x=l ,
u (x,t) t >0
.
u (x,t) =X (x) T (t)
,
[0, l ]. - ,
-
,
, ,
,
, Bk= 0,
232. l , - 0. u (r,t) , -
.
v (r) -
, ,