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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1994 • Question 10

Question

Math 6420 • PDE Fall 1994 • Question 10

Find the Green’s function for the Poisson equation \(\Delta u=f\) in the infinite strip \(0\le y\le 1\), \(-\infty <x<\infty \) with boundary data \(u(x,0)=0\) and \(u(x,1)=1\). Then solve the problem (in quadrature) if \(f(x,y)=y(1-y)e^{-x^2}\).

Raw LaTeX

Find the Green's function for the Poisson equation
\(\Delta u=f\) in the infinite strip \(0\le y\le 1\), \(-\infty<x<\infty\) with boundary data
\(u(x,0)=0\) and \(u(x,1)=1\). Then solve the problem (in quadrature) if
\(f(x,y)=y(1-y)e^{-x^2}\).

Topic Tags

Distributions and Weak Solutions Numerical Quadrature Poisson Equation Quadrature Rules