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 $u(x, t)$.
Chdogordon
153
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
Martin
737
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 757 views
- $12.00
Related Questions
- Two masses attached to three springs - Differential equations
- Why does this spatial discretization with n intervals have a position of (n-1)/n for each interval?
- Differential equations 2 questions with multiple parts
- Solve the two-way wave equation in terms of $u_0$
- How should I approach this question?
- General solutions of the system $X'=\begin{pmatrix} a & b \\ c & d \end{pmatrix} $
- Integral of the fundamentla solution of the heat equation
- Derive the solution $u(x,t)=\frac{x}{\sqrt{4 \pi}} \int_{0}^{t} \frac{1}{(t-s)^{3/2}}e^{\frac{-x^2}{4(t-s)}}g(s) \, ds$ for the heat equation
