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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2018 • Question 7

Question

Math 6420 • PDE Fall 2018 • Question 7

Solve Laplace’s equation \(\phi _{xx}+\phi _{yy}=0\) in the domain \[ D=\{(x,y)\in \mathbb {R}^2:x^2+y^2>1,\ (x+2)^2+y^2<9\} \] with boundary conditions: \(\phi (x,y)=a\) when \(x^2+y^2=1\) and \(\phi (x,y)=b\) when \((x+2)^2+y^2=9\).

Raw LaTeX

Solve Laplace's equation \(\phi_{xx}+\phi_{yy}=0\) in the domain
\[
  D=\{(x,y)\in\mathbb{R}^2:x^2+y^2>1,\ (x+2)^2+y^2<9\}
\]
with boundary conditions: \(\phi(x,y)=a\) when \(x^2+y^2=1\) and \(\phi(x,y)=b\) when
\((x+2)^2+y^2=9\).

Topic Tags

Boundary Value Problems Finite Difference Boundary Value Problems Laplace Equation Linear Programming and Optimization