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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2010 • Question 6

Question

Math 6420 • PDE Spring 2010 • Question 6

Find a solution \(u(x,y)\) of Laplace’s equation on the domain \(-\infty <x<\infty \), \(0<y<\infty \) for which \(u(x,0)=x^{1/2}\) for \(0<x<\infty \). What is \(u(x,0)\) for \(-\infty <x<0\)?

Raw LaTeX

Find a solution \(u(x,y)\) of Laplace's equation on the domain \(-\infty<x<\infty\),
\(0<y<\infty\) for which \(u(x,0)=x^{1/2}\) for \(0<x<\infty\). What is \(u(x,0)\) for
\(-\infty<x<0\)?

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Laplace Equation Linear Programming and Optimization