Question

Solve the following system of partial differential equations on - <r<0. u + 1x + 70, +6w 24-U: +3w, W -2 u(,0) v(3,0) w(1,0) = = = = = = 0. 0. 0. 10(E). (). (x).

Answer 1

Solusion given 44 tym + 7 Vn't Gonto V - Vn + 3Wnso - ou V wfm2 on a worden . Ut ulnio) - Yoln) - Correio Unio) = Volm Win10) s Wolm) pom can ton J9Wt - 2Wm=0 let's say n = x-qt sted Tor a bixed n ns at th Now we can write wie it) = (mit), t) dt at dwg wx + Wt du to this, sokerion w is constant calony Curves n-gt= from insical condition wln10) = Woln) ns Wolf

So solusion of eas is 12-2¢= Wold Twint) = wo (2-26) Now Toom eq © VE - Vn +3wn to Wn = wo Vt - Vn #3wo so Vf = Vre-300 Simahy Assumme = x-tt3wo n = n+t - 3wo solusion from insical condition Vinio) = ro TVimit) s Volde-t +3wo) -Now fomegn (1 uftum + 7 Va town to + ₂ + 7 + 660o = 0 so four intial condition u 1260) = 40lm) and up = -44 -7% -6 wo X = n - t+frotowo Tu= uo (KH-70 -6 Wola