Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2018 • Question 5

Question

Math 6420 • PDE Fall 2018 • Question 5

Let \(\delta \in \mathcal {D}'(\mathbb {R})\) denote the ‘delta function’. Find \(u\in \mathcal {D}'(\mathbb {R})\) that solves the following linear partial differential equation: \[ \partial ^2 u=\delta . \] Is the solution unique?

Hint: You can solve this equation by guessing the distribution and then verifying that is solves the equation.

Raw LaTeX

Let \(\delta\in\mathcal{D}'(\mathbb{R})\) denote the `delta function'. Find
\(u\in\mathcal{D}'(\mathbb{R})\) that solves the following linear partial differential
equation:
\[
  \partial^2 u=\delta.
\]
Is the solution unique?

\textit{Hint:} You can solve this equation by guessing the distribution and then verifying
that is solves the equation.

Topic Tags

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