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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1998 • Question 4

Question

Math 6420 • PDE Fall 1998 • Question 4
Solve the differential equation in the sense of distributions \[ xu'=\delta(4x^2-1),\qquad x\in[-1,1],\qquad u(-1)=1,\qquad u(1)=0. \] Discuss why two boundary conditions are provided for the first order differential equation.

Raw LaTeX

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

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