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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1999 • Question 2

Question

Math 6420 • PDE Fall 1999 • Question 2

Solve the differential equation in the sense of distributions \[ xu'=\delta (x^4-1),\qquad x\in [-2,2],\qquad u(-2)=u(2)=0. \] Discuss why two boundary conditions are provided for the first order differential equation.

Raw LaTeX

Solve the differential equation in the sense of distributions
\[
  xu'=\delta(x^4-1),\qquad x\in[-2,2],\qquad u(-2)=u(2)=0.
\]
Discuss why two boundary conditions are provided for the first order differential equation.

Topic Tags

Boundary Value Problems Distributions and Weak Solutions Fundamental Solutions Linear Programming and Optimization