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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2017 • Question 7

Question

Math 6420 • PDE Fall 2017 • Question 7

Find the real-valued function \(\Phi (z)\) that solves Laplace’s equation in the region between the two noncentric circles \(\lvert z\rvert =1\) and \(\lvert z-1\rvert =\frac {5}{2}\) subject to the boundary conditions \(\Phi =0\) on \(\lvert z\rvert =1\) and \(\Phi =1\) on \(\lvert z-1\rvert =\frac {5}{2}\).

Raw LaTeX

Find the real-valued function \(\Phi(z)\) that solves Laplace's equation in the region
between the two noncentric circles \(\lvert z\rvert=1\) and
\(\lvert z-1\rvert=\frac{5}{2}\) subject to the boundary conditions \(\Phi=0\) on
\(\lvert z\rvert=1\) and \(\Phi=1\) on \(\lvert z-1\rvert=\frac{5}{2}\).

Topic Tags

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