.
(24.4)
. (24.5)
(24.4) (24.5) . , t. (24.5)
(24.6)
.
, (24.7)
. . (24.6) , ; . , .. . . , ji(t) , yi = xi(t) ji(t) , ji(t) . , . : n=2:
2) k 1 ¹ k 2, k 1 > 0, k 2 > 0
3) k 1 ¹ k 2, k 1 > 0, k 2 < 0
. . .
.
(24.4)
. (24.5)
(24.4) (24.5) . , t. (24.5)
(24.6)
.
, (24.7)
. . (24.6) , ; . , .. . . , ji(t) , yi = xi(t) ji(t) , ji(t) . , . : n=2:
|
|
() ()
()
.
26. .
27. .
28. 1- :
, , ,
+ 8 =0, + 2 =0 ∞ <x< +∞ 0 <t< ∞
(x, 0) = f(x), (x, 0) = d(x)
, x t . .
+ =
+ A = (8.7)
A = = = =
v = u = pv, p- , .
:
det (A λ E)=0
= 0 ó 16 = 0 = 4 = - 4
= 4
(A E) () = 0 = =1, =2 => ,- = - 4
= = 1, = - 2
P= = = det p= 4
AP = = = = B
, u=pv v . u=pv , , v, u=pv :
= p = p (8.8)
(8.8) : + A = 0
+ AP = 0 │*
+ A =0; + B = 0 (8.9)
, B
(8.9) : (8.10)
2 , , : + =0
- =0 = x- 4t = = ϕ (x-4t) : = x+4t = = (x+4t)
:u=pv
= =
(x, t) =
(x, t) =
:
│
4 = +2 (x) = (f(x)+2g(x)) 4 Ψ(x)= 2 , Ψ(x)= (2g(x)- f(x)) =>
: (x, t) = (f(x-4t)+2g(x-4t))- (2g(x+4t)-f(x+4t)) (x, t) = (f(x-4t)+2g(x-4t)+ (2g(x+4t)-f(x+4t))
: , , - .
29. .