F t Crdr Linar % kms
PDE Djenai|atrorn
Chysdor 29
Lt
ER
H t 4 , t 22x t
+ n x
(
n
/9
un
\Unl
a.
A-()d
Wit
T A U =0
Caled
Case
n-dirusimal
/42
btrzain
Lr ,
DLt<
-
transp ort e n
A dDna,ie
4+
frem eangom alone
ht*
Each PpE a
0
oit
x=0, u(x,Ol=DA)
ax =0 ,uA0)
In
a)
tranSt
t
4,xt) Glx4,t)
e
urti-f-el/
ulat)= t(-4;t)
sien
2
A dtiezoral rabl
a adingone! m a t i A
Smlar
Case 2
A
ie,
there 1s an invertible maTxPan.! a dngene
matrr A
s,t.
AP=A
t u n s out,inthiscase,
tialt Aste drazonm
)
eg[A
(
;
:
FA
(ev)
envaelaes
Ps
Te matra
whose columns
epenedos (e.)
re
Vze7(A)
are
This
as
case
H e tonrespoolg
nespoolir
the
°
,%resp
oreguvebestr
-AL)-0,%erep
A veAy
(A-AT) V=0
be reducec 7
fhe preudus
hulbplp. H-PDE
folys
(A)
det(A
det (A -AZ)-0
he solufrims
olbtrned bg solvite
Can
and
,
e.
=
col;(P)
,ie,
otA
elA)
o)e
ponolng
cerme
e.v.(A)
are
ratn
dme
H ef
P
APP"
AI=
b
nd replae
+AP P u =
A
t
-
y+APu,0
lvatu Ciu=P) gefF
wth A
lva,o)-P ut,o)-Pqo)= Ya)
dag
Solve fer
V
Asin
Cae
1), 0bain
xtY(1-1t) ,/eis
Finally
bxanple
-
Pv
t8 x
S l w e E 4 tt 2
uyx,o)=
In mam
0
&)
/0
fosm
K
Up
4+A- 0
sandard
4-/)
Jt(A-AI)-JA/-A
)** | - 4,+
,=t
2
V.A)
(V
evA)=M:A-,1V=0 ,ie., 2 4/ / )
( tv +8v2=0
2
+4u,0
eA
2V2V
V
-2V
arbitny
cel P)
e.7(A)-v
A-11)V=0,ie
-4yroy-0
(-4
)
2 -t
2y-45=0
eZA-()-
22
arb.
P
2
(
H
ere weve useol
det
Wh
V=%
-2
2
fact
)- ad-be
to, Hon [
ineble
our DE PPrblen
AV
Lv,ol-fu( *
The dul, -jcarn l,
s
Kr)--14)=Xr-H) Gh.d)51-1E)
Fnaly
ub,0
(-2 2 )/%44
-2 +2
Kemarks
Thue e,v(A) Can be ploced at
Z , bu he corespondng
in P
tordn
be
a
placed
evA)hane fo
any crler
in
reple fA=
Hen
d Heren7A
Tm
nser
H
P)
2
-1
2 /
tme)
befone
ot Re PDE pnvblem nlbethe
eady tde Jolafio
sam.
he
Decduce tron eabow
/VP
Oste
paRL
HT Salve Ex
Submit Hw/
email
30,23
husdy Be
b:00 pn ,husdy
