affix.toheo.ali c uo fp e

t

sofgducx.tI xet

sni.x i

kskkohd.LItH xe2tL

2 dat o dat 2 u ftptotttHUo gU.lx 1 HtauhCx

nuWI

x

tshow

thu5

compntets.to dff o dxq o

dfu ddI FtfIoxo o

d4dx U'olio

dia Hd oc uo cx

soured

teaU Seth XoUo o

1.1 t

X.tt shockx.tt 2 Yo wow

Hatei

2T

3 ha u

fi I

Sketchofcharacterirt

It

Maple code for plotting

Snatch of soda thou

e u t o

tHo

u u e

withdxqt U.it x u e

tc

X xotx

att

x xotu.li et

sketchA Xo o nee

I geti u

B x L no o EffCE X 3 u z

x z tEct EtU z e

t 4 x i u

f ohSolIsnetde

Noshock l

c u dxqt.ua u u.et x x uoletT

iat o

o no 1

x et L u et u

XH.atxo i uo x L 4 0

ato z u yet u Eet a x

A B C all intersect when K 2 xLfC

eI

4 As in class inner solin las formucx.tl Uly y

x

Then we get sUy Utley U Ugh

go at leading order we justgetICH Uy t UU y Ugg

As in class notes it follows thatsht Uttz where U

are the values of u to the left andto the right of the interface

Now the outer problem is justU t t

U U U n O so as in

peer q dug u along characteristicsU

Then w u

From ix c u IO

U O X 0

Thus u o and u

thus dsa

so that qsH eI

a

numericala

SCH

VS humerig

Excellent agreement