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Boundary-Value Problems in Other Coordinate Systems Solve ∆u = 0 in a disk x^2 + y^2...

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Advance Math

Boundary-Value Problems in Other Coordinate Systems

  1. Solve ∆u = 0 in a disk x^2 + y^2 ≤ 25, where u(5, θ) = 7 sin 3θ− 6 sin 8θ and u is bounded when   r = 0.
  2. Solve ∆u = 0 in an annulus 1 ≤ x^2+y^2 ≤ 4, where u(1, θ) = 75sin θ, u(2, θ) = 60 cos θ.
  3. Find the steady-state temperature distribution in a disk ofradius 1 if the upper half of the circumference is kept at 100â—¦ andthe lower half is kept at 0â—¦ .

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