0
$\begingroup$

The system of conservation laws in one dimension (i.e. $x \in \mathbb{R}$) is given (in the conservative form): $$\partial_t U + \partial_x F(U)=0.$$

What exactly is quasilinear form of this system and when is it possible to write it from conservative form? Also, is DF(U) always linear?

  • 0
    $DF(U)$ is, by definition of the derivative, a linear map $\mathbb R^d \to \mathbb R^d$, so $DF(U)\partial_x U$, is linear in $\partial_x U$, note that $DF(U)\partial_x U$ is in general not linear in $U$.2012-09-26

1 Answers 1

0

I accidentally find the answer $ U_t+A(U)U_x=0 $ where $A=F'$

referring to page 2 in https://www.math.psu.edu/bressan/PSPDF/clawtut09.pdf