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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2000 • Question 9

Question

Math 6410 • ODE Fall 2000 • Question 9

Give the heat equation on a semi-infinite rod with initial temperature \(g(x)\) and Dirichlet boundary conditions. Apply the method of odd extension of the heat kernel formula for \((-\infty ,\infty )\) to derive a formula for the solution.

Raw LaTeX

Give the heat equation on a semi-infinite rod with initial temperature \(g(x)\) and
Dirichlet boundary conditions. Apply the method of odd extension of the heat kernel
formula for \((-\infty,\infty)\) to derive a formula for the solution.

Topic Tags

Boundary Value Problems Boundary Value Problems and Sturm-Liouville Theory Heat Equation and Parabolic Equations Poincare Maps and Periodic Solutions