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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2014 • Question 1

Question

Math 6420 • PDE Spring 2014 • Question 1

Consider the problem \(u''(x)=x\delta '(x)\), where \(\delta \) is the “delta function”. Explain what it means for this problem to have a solution \(u\) in the sense of distributions. Find a distributional solution \(u\) and prove that it does in fact solve the problem in the sense of distributions.

Raw LaTeX

Consider the problem \(u''(x)=x\delta'(x)\), where \(\delta\) is the ``delta function''.
Explain what it means for this problem to have a solution \(u\) in the sense of distributions.
Find a distributional solution \(u\) and prove that it does in fact solve the problem in the
sense of distributions.

Topic Tags

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