Question: 1. (10 Points) (Reduction to Zero BC): Solve Ut = Duxx u|x=0= To, u|x=L = T (T, T constants) ult=0 = f(x), in three

1. (10 Points) (Reduction to Zero BC): Solve Ut = Duxx u|x=0= To, u|x=L = T (T, T constants) ult=0 = f(x), in

1. (10 Points) (Reduction to Zero BC): Solve Ut = Duxx u|x=0= To, u|x=L = T (T, T constants) ult=0 = f(x), in three steps: Step 1. Construct a linear function T(x) of x such that T(0) = T and T(L) = T. Step 2. Solve a new auxillary v(t, x) with a zero BC problem and a modified initial conditions: Vt = Dvxx v|x=0 = v|x= L = 0 v|t=0= f(x) - T(x). Step 3. Show u(t, x) = v(t, x) +T(x).

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