Question

Solve
Ut = u
for for $t \geq 0$ and for . Determine and and look at their magnitudes. Note that when , we are looking at the backward heat equation and given the magnitude of , what can you say about the solution to the backward heat equation?

Answer 1

Ut = White. Ulot)- U11.+33.0 U(Ho) = 108 sinc 10tnx)=fits uinta- & onenin't ginnat UCH+) = I on sinnati ennet n=1

Dr = 2 L sincroniti) Sinnan de 1 let nhat nana di Da alimentos eingeart) - Jinnt + De ce sa sin cie's). Sinna but also and "Sihmt. sinnti doo To if man if mai - TV2 it mth Pa = Toen toe Dr = 0 &non l {1o7d.

Utd, 1) = 0, 8h ( sºnk) e loºns Lustit a to ve sincional. e lolar? U(H. 3) = = sin court). 10*n*x3 Joe U (4,3) = sin ciutrit.). Toen e Saxo 3n8x1014 I tuxwurd heut ] [ę? U14.-3) = = sin cielna). e3nxioly backward - heat equation TUCH.3) 1 < 1UCH ) 1 farwurd heat Eqr. backward heat Equation.