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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2004 • Question 1

Question

Math 6420 • PDE Spring 2004 • Question 1

  1. Prove that \(x\delta (x)=0\) in the sense of distribution.
  2. Formulate the differential equation \(xu'-u=0\) as a problem in the sense of distribution and find its general solution, also in the sense of distribution.

Raw LaTeX

\begin{enumerate}
\item[(a)] Prove that \(x\delta(x)=0\) in the sense of distribution.
\item[(b)] Formulate the differential equation \(xu'-u=0\) as a problem in the sense of
distribution and find its general solution, also in the sense of distribution.
\end{enumerate}

Topic Tags

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