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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1999 • Question 11

Question

Math 6420 • PDE Fall 1999 • Question 11

Find the bounded solution \(u(x,y)\) of the Laplace equation in the sector \[ D=\{(r,\theta ): 0<\theta <3\pi /4\}\qquad (x+iy=z=re^{i\theta }) \] satisfying the boundary conditions \[ u=0\text { when }\theta =0,\qquad u=5\text { when }\theta =\frac {3\pi }{4}. \]

Raw LaTeX

Find the bounded solution \(u(x,y)\) of the Laplace equation in
the sector
\[
  D=\{(r,\theta): 0<\theta<3\pi/4\}\qquad (x+iy=z=re^{i\theta})
\]
satisfying the boundary conditions
\[
  u=0\text{ when }\theta=0,\qquad u=5\text{ when }\theta=\frac{3\pi}{4}.
\]

Topic Tags

Boundary Value Problems Distributions and Weak Solutions Laplace Equation Linear Programming and Optimization