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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2014 • Question 5

Question

Math 6420 • PDE Spring 2014 • Question 5

Construct the Green’s function for the problem \[ u''(x)+\alpha ^2u(x)=f(x),\quad \text {on }(0,1),\qquad u(0)=u(1)=0. \] Write the solution \(u\) in terms of the Green’s function, and determine values of \(\alpha \) for which the Green’s function does not exist.

Raw LaTeX

Construct the Green's function for the problem
\[
  u''(x)+\alpha^2u(x)=f(x),\quad \text{on }(0,1),\qquad u(0)=u(1)=0.
\]
Write the solution \(u\) in terms of the Green's function, and determine values of \(\alpha\)
for which the Green's function does not exist.

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Fundamental Solutions Linear Programming and Optimization