# Find a formula for the vector hyperbolic problem

$u_t + Au_x = ?u$

$A=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} $

with $u = (u, v)^T$ (transpose to indicate u is a column vector in the equation above).

Find a formula using characteristics for the problem with given initial data $u(x, 0) = u_0(x)$.

Reformulate the vector problem as a second-order scalar problem for $u(x, t)$.

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

1 Attachment

The answer is accepted.

- answered
- 160 views
- $12.00

### Related Questions

- Use the divergence theorem to derive Green's identity
- Find solutions to the Riemann Problems
- Burgers’ equation $u_t + u u_x = −x $
- Explicit formula for the trasport equation
- Solve the Riemann Problem
- Beginner Differential Equations - Growth Rate Question
- Solve $Lx = b$ for $x$ when $b = (1, 1, 2)^T$.
- How does the traffic flow model arrive at the scaled equation?