2 ® Consider the heat equation den d²u dx? with xe to,!). ond B.C. u(t,0)=0, au dx (6,1)=0. Show that it m(t, x)= TC IXC

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2 Consider The Heat Equation Den D U Dx With Xe To Ond B C U T 0 0 Au Dx 6 1 0 Show That It M T X Tc Ixc 1 (291.78 KiB) Viewed 25 times

2 ® Consider the heat equation den d²u dx? with xe to,!). ond B.C. u(t,0)=0, au dx (6,1)=0. Show that it m(t, x)= TC IXCX), then x"(x) = X with x(0=0, x',)= x(x) for some XER b Show that xso implies <(k)=0. ht no © * - (+um), na © Shaw that the only admissible Xs are given by the ( ²6&n]t and correspondingly Mn CE,X DE Tn (t]Xnx)= é sin ( + nT )x) of +