advertisement

M 545 Homework Problem Due Monday Oct 25 Suppose u = ux, y solves ∇ 2 ux, y = 0 x ∈ R, y > 0 ux, 0 = I 1/4 x − 1/2 x∈R and v = vx, y solves ∇ 2 vx, y = 0 0 < x < 1, 0 < y < 1 vx, 0 = I 1/4 x − 1/2, 0 < x < 1, vx, 1 = 0 , 0 < x < 1, ∂ x v0, y = ∂ x v1, y = 0 1. Is u 1 , 1 2 2 0 < y < 1. less than, equal to, or larger than v 1 , 1 ? 2 2 2. Does the difference u 1 , y − v 1 , y change sign on 0 < y < 1? 2 2 3. How would you explain your results in the first two questions?e.g. in the context of two heat conduction experiments what do your results mean? 1