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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1999 • Question 20

Question

Math 6410 • ODE Fall 1999 • Question 20

Apply the above result to the initial boundary value problem \[ \begin {aligned} u_t-u_x&=0,\qquad t>0,\ x\in \mathbb {R},\\ u(0,x)&=g(x),\qquad x\in \mathbb {R}. \end {aligned} \] Solve this problem explicitly.

Also state a result about the initial value problem \[ \begin {aligned} u_t-u_x&=f(t,x),\qquad t>0,\ x\in \mathbb {R},\\ u(0,x)&=g(x),\qquad x\in \mathbb {R}. \end {aligned} \]

Raw LaTeX

Apply the above result to the initial boundary value problem
\[
\begin{aligned}
  u_t-u_x&=0,\qquad t>0,\ x\in\R,\\
  u(0,x)&=g(x),\qquad x\in\R.
\end{aligned}
\]
Solve this problem explicitly.

Also state a result about the initial value problem
\[
\begin{aligned}
  u_t-u_x&=f(t,x),\qquad t>0,\ x\in\R,\\
  u(0,x)&=g(x),\qquad x\in\R.
\end{aligned}
\]

Topic Tags

Boundary Value Problems Boundary Value Problems and Sturm-Liouville Theory Existence and Uniqueness Theorems