Question

Part 1 of 1 Question 1 of 1 50.0 Points Mark which statements below are true, using the following Consider the diffusion problem, дги ди dx2dt u(x,O)-f(x) where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is a transient part and a steady state part. From this we can proceed to separate u(x, t)-X(x)T(t) + us(x), where the subscript designates the function as the steady limit and does not represent a derivative BEWARE: MARKING A STATEMENT TRUE THAT IS ACTUALLY FALSE RECEIVES A NEGATIVE MARK! A. The time part of the solution is obtained by solving the following BVP B. Substituting the alternative split form of a solution with transient and steady parts gives u (x) X"(x)T()X(x)T() Ос. The functions of the set sinn 1,2,3,...) are orthogonal on [0, L] For the functions of the set (sinn 1,2,3,...) zero and negative values of 7n are not considered because they are not orthogonal E. Upon separation of variables, the time problem is given by OF u(x, t)-u, (x) cannot be represented by a Fourier series because normal separability does not work. G. lim 14 (x, t) -+00 0 lu cannot satisfy u(0, t) = 0, u(L, t) = 50 OI. The steady state solution is 50 u,(x)-x+ Fx(r - L) The full solution is u(x,t)=us(x) + 〉 c, sin(-) exp{- where 50τ し,2

Answer 1

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Correct answer = B , C ,E , G

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