M 545 Homework Problem
Due Monday Oct 25
Suppose u = ux, y solves
∇ 2 ux, y = 0
x ∈ R, y > 0
ux, 0 = I 1/4 x − 1/2
x∈R
and v = vx, y solves
∇ 2 vx, y = 0
0 < x < 1, 0 < y < 1
vx, 0 = I 1/4 x − 1/2, 0 < x < 1,
vx, 1 = 0
, 0 < x < 1,
∂ x v0, y = ∂ x v1, 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