2

I don't know what to do, normally we'd do $u_t=G_t$ and $u_{xx}=\left(G_x\right)^2$ (so we can have a "quadratic equation" and compute the discriminant) but then we'd have to divide it by $\left(G_t\right)^2$ because of $u=u\left(x,t\right)$, which would give us something I'm not used to ($\frac{1}{G_t}$). Also I don't know what to do with the $u$ here

user
  • 53

1 Answers1

2

Wikipedia tells me the following. A PDE $$au_{xx} + bu_{xt} + cu_{tt} + du_x + eu_t +fu= g$$ is

  • Elliptic, if $b^2-4ac<0$
  • Hyperbolic, if $b^2-4ac >0$
  • Parabolic, if $b^2-4ac = 0$

In your case, $a = -1$, $b = 0$, and $c = 0$, so $b^2-4ac = 0$ and the PDE is parabolic.

Is it as simple as this?

MPW
  • 43,638
  • Thanks, we did it but without $du_x$, $eu_t$ and $fu$ on the left side, we just dragged it over to the right side (so it's included in our g) – user Apr 28 '21 at 19:19