Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Spring 2017 • Question 6

Question

Math 6410 • ODE Spring 2017 • Question 6

Does the partial differential equation \[ \frac {\partial u}{\partial t}-\frac {\partial u}{\partial x}=-u \] subject to the restriction that \(u=\exp (-x^2)\) on the curve \(t=x^2\) have a solution? If it does have a solution, indicate for what ranges of \(x\) and \(t\) this solution is uniquely defined and if it does not have a solution, explain why.

Raw LaTeX

Does the partial differential equation
\[
  \frac{\partial u}{\partial t}-\frac{\partial u}{\partial x}=-u
\]
subject to the restriction that \(u=\exp(-x^2)\) on the curve \(t=x^2\) have a
solution? If it does have a solution, indicate for what ranges of \(x\) and \(t\) this
solution is uniquely defined and if it does not have a solution, explain why.

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Fundamental Solutions Poincare Maps and Periodic Solutions