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@ A B C D 1 ˙ ˝ E F " G H I J K , L M N O P Q R S T U V W X Y Z. 5 (Logan, 24 # 1) Solve the problem ut =kuxx, x >0, t >0, ux(0,t)=0, t >0, u(x,0)=φ(x), x >0, with an insulated boundary condition by extending φ to all of the real axis as an even function The solution is u(x,t)= Z ∞ 0 G(x −y,t)G(x y,t)φ(y)dy First note that the solution to the IVP ut = kuxx, −∞ < x < ∞, t > 0, u(x,0) = f(x), −∞. 0 l en0` K I ps &* E4 V@` \ H 6 !P> > p a h^ hQ 0 l en0 ?1 ps &* I E "z @?.
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