2
$\begingroup$

The Burgers' equation is given by $u_{t}+uu_{x}=\nu u_{xx}$, where $u=u(x,t)$ and $\nu$ is the kinematic viscosity.

How do I rewrite the equation (or any higher order PDE) as a system of first-order quasilinear PDEs? I am particularly interested in a general methodology. Books or online materials that discuss this in detail will be appreciated.

Thanks, Radz.

$\endgroup$
  • 2
    $\begingroup$ Try the transformation $u = -2\nu\frac{\partial \log F}{\partial x}$ under which the equation transforms into the linear diffusion equation $\frac{\partial F}{\partial t} = \nu \frac{\partial^2 F}{\partial x^2}$ (modulo a integration constant). $\endgroup$ – Winther Aug 18 '14 at 14:43
  • 1
    $\begingroup$ Dear @Winther. Thanks. I added the Burger's equation just for argument sake and did not know that there was such a transformation! $\endgroup$ – Radz Aug 22 '14 at 12:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.