Find a formula for the vector hyperbolic problem
Consider 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 $u(x, t)$.
$u_t + Au_x = −u$
$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 $u(x, t)$.
Chdogordon
153
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Martin
1.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1869 views
- $12.00
Related Questions
- Power series solution of Differential Equations
- Show that the following subset Ω of Euclidean space is open
- Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
- Differential equations
- Conservative system ODE
- Show that $\int_\Omega \Delta f g = \int_\Omega f \Delta g$ for appropriate boundary conditions on $f$ or $g$
- Find the General Solution
- Differential equations, question 5
