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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2001 • Question 9

Question

Math 6420 • PDE Fall 2001 • Question 9

Find an integral representation for the solution of the telegrapher’s equation \[ u_{tt}+au_t+bu=u_{xx} \] with \(u(0,t)=f(t)\) and \(u_x(0,t)=g(t)\) specified for all time.

Raw LaTeX

Find an integral representation for the solution of the telegrapher's equation
\[
  u_{tt}+au_t+bu=u_{xx}
\]
with \(u(0,t)=f(t)\) and \(u_x(0,t)=g(t)\) specified for all time.

Topic Tags

Cauchy Integral Formula and Integral Theorems Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Linear Programming and Optimization